Publications in international journals
Martin Vohralík


Papers published or accepted for publication

2024

1.   Mitra, K., and Vohralík, M. A posteriori error estimates for the Richards equation. Math. Comp. 93, 347 (2024), 1053–1096. Journal version, preprint PDF icon.

2.   Gantner, G., and Vohralík, M. Inexpensive polynomial-degree-robust equilibrated flux a posteriori estimates for isogeometric analysis. Math. Models Methods Appl. Sci. 34, 3 (2024), 477–522. Journal version, preprint PDF icon.

3.   Févotte, F., Rappaport, A., and Vohralík, M. Adaptive regularization, discretization, and linearization for nonsmooth problems based on primal-dual gap estimators. Comput. Methods Appl. Mech. Engrg. 418, B (2024), 116558. Journal version, preprint PDF icon.

2023

4.   Chaumont-Frelet, T., and Vohralík, M. p-robust equilibrated flux reconstruction in H(curl) based on local minimizations. Application to a posteriori analysis of the curl–curl problem. SIAM J. Numer. Anal. 61, 4 (2023), 1783–1818. Journal version, paper PDF icon.

5.   Jayadharan, M., Kern, M., Vohralík, M., and Yotov, I. A space-time multiscale mortar mixed finite element method for parabolic equations. SIAM J. Numer. Anal. 61, 2 (2023), 675–706. Journal version, paper PDF icon.

6.   Daniel, P., and Vohralík, M. Guaranteed contraction of adaptive inexact hp-refinement strategies with realistic stopping criteria. ESAIM Math. Model. Numer. Anal. 57, 1 (2023), 329–366. Journal version, preprint PDF icon.

7.   Ben Gharbia, I., Ferzly, J., Vohralík, M., and Yousef, S. Adaptive inexact smoothing Newton method for a nonconforming discretization of a variational inequality. Comput. Math. Appl. 133 (2023), 12–29. Journal version, preprint PDF icon.

8.   Ben Gharbia, I., Ferzly, J., Vohralík, M., and Yousef, S. Semismooth and smoothing Newton methods for nonlinear systems with complementarity constraints: Adaptivity and inexact resolution. J. Comput. Appl. Math. 420 (2023), 114765. Journal version, preprint PDF icon.

2022

9.   Ern, A., Gudi, T., Smears, I., and Vohralík, M. Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H(div). IMA J. Numer. Anal. 42, 2 (2022), 1023–1049. Journal version, preprint PDF icon.

10.   Papež, J., and Vohralík, M. Inexpensive guaranteed and efficient upper bounds on the algebraic error in finite element discretizations. Numer. Algorithms 89 (2022), 371–407. Journal version, preprint PDF icon.

11.   Chaumont-Frelet, T., Ern, A., and Vohralík, M. Stable broken H(curl) polynomial extensions and p-robust a posteriori error estimates by broken patchwise equilibration for the curl–curl problem. Math. Comp. 91, 333 (2022), 37–74. Journal version, preprint PDF icon.

2021

12.   Chaumont-Frelet, T., and Vohralík, M. Equivalence of local-best and global-best approximations in H(curl). Calcolo 58 (2021), 53. Journal version, free view-only version, preprint PDF icon.

13.   Cancčs, E., Dusson, G., Maday, Y., Stamm, B., and Vohralík, M. Post-processing of the planewave approximation of Schrödinger equations. Part I: linear operators. IMA J. Numer. Anal. 41, 4 (2021), 2423–2455. Journal version, preprint PDF icon.

14.   Chaumont-Frelet, T., Ern, A., and Vohralík, M. On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation. Numer. Math. 148, 3 (2021), 525–573. Journal version, preprint PDF icon.

15.   Miraçi, A., Papež, J., and Vohralík, M. A-posteriori-steered p-robust multigrid with optimal step-sizes and adaptive number of smoothing steps. SIAM J. Sci. Comput. 43, 5 (2021), S117–S145. Journal version, paper PDF icon.

16.   Haberl, A., Praetorius, D., Schimanko, S., and Vohralík, M. Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver. Numer. Math. 147, 3 (2021), 679–725. Journal version, preprint PDF icon.

17.   Miraçi, A., Papež, J., and Vohralík, M. Contractive local adaptive smoothing based on Dörfler’s marking in a-posteriori-steered p-robust multigrid solvers. Comput. Methods Appl. Math. 21, 2 (2021), 445–468. Journal version, preprint PDF icon.

18.   Cancčs, C., Nabet, F., and Vohralík, M. Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations. Math. Comp. 90, 328 (2021), 517–563. Journal version, preprint PDF icon.

19.   Ern, A., Vohralík, M., and Zakerzadeh, M. Guaranteed and robust L2-norm a posteriori error estimates for 1D linear advection problems. ESAIM Math. Model. Numer. Anal. 55 (2021), S447–S474. Journal version, preprint PDF icon.

2020

20.   Chaumont-Frelet, T., Ern, A., and Vohralík, M. Polynomial-degree-robust H(curl)-stability of discrete minimization in a tetrahedron. C. R. Math. Acad. Sci. Paris 358, 9–10 (2020), 1101–1110. Journal version, preprint PDF icon.

21.   Miraçi, A., Papež, J., and Vohralík, M. A multilevel algebraic error estimator and the corresponding iterative solver with p-robust behavior. SIAM J. Numer. Anal. 58, 5 (2020), 2856–2884. Journal version, paper PDF icon.

22.   Cancčs, E., Dusson, G., Maday, Y., Stamm, B., and Vohralík, M. Guaranteed a posteriori bounds for eigenvalues and eigenvectors: multiplicities and clusters. Math. Comp. 89, 326 (2020), 2563–2611. Journal version, preprint PDF icon.

23.   Papež, J., Rüde, U., Vohralík, M., and Wohlmuth, B. Sharp algebraic and total a posteriori error bounds for h and p finite elements via a multilevel approach. Recovering mass balance in any situation. Comput. Methods Appl. Mech. Engrg. 371 (2020), 113243. Journal version, preprint PDF icon.

24.   Dabaghi, J., Martin, V., and Vohralík, M. Adaptive inexact semismooth Newton methods for the contact problem between two membranes. J. Sci. Comput. 84 (2020), 28. Journal version, preprint PDF icon.

25.   Smears, I., and Vohralík, M. Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction–diffusion problems. ESAIM Math. Model. Numer. Anal. 54, 6 (2020), 1951–1973. Journal version, preprint PDF icon.

26.   Blechta, J., Málek, J., and Vohralík, M. Localization of the W-1,q norm for local a posteriori efficiency. IMA J. Numer. Anal. 40, 2 (2020), 914–950. Journal version, preprint PDF icon.

27.   Dabaghi, J., Martin, V., and Vohralík, M. A posteriori estimates distinguishing the error components and adaptive stopping criteria for numerical approximations of parabolic variational inequalities. Comput. Methods Appl. Mech. Engrg. 367 (2020), 113105. Journal version, preprint PDF icon.

28.   Ern, A., and Vohralík, M. Stable broken H1 and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions. Math. Comp. 89, 322 (2020), 551–594. Journal version, preprint PDF icon.

29.   Ben Gharbia, I., Dabaghi, J., Martin, V., and Vohralík, M. A posteriori error estimates for a compositional two-phase flow with nonlinear complementarity constraints. Comput. Geosci. 24 (2020), 1031–1055. Journal version, preprint PDF icon.

30.   Daniel, P., Ern, A., and Vohralík, M. An adaptive hp-refinement strategy with inexact solvers and computable guaranteed bound on the error reduction factor. Comput. Methods Appl. Mech. Engrg. 359 (2020), 112607. Journal version, preprint PDF icon.

31.   Mallik, G., Vohralík, M., and Yousef, S. Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers. J. Comput. Appl. Math. 366 (2020), 112367. Journal version, preprint PDF icon.

2019

32.   Ahmed, E., Ali Hassan, S., Japhet, C., Kern, M., and Vohralík, M. A posteriori error estimates and stopping criteria for space-time domain decomposition for two-phase flow between different rock types. SMAI J. Comput. Math. 5 (2019), 195–227. Journal version, preprint PDF icon.

33.   Ern, A., Smears, I., and Vohralík, M. Equilibrated flux a posteriori error estimates in L2(H1)-norms for high-order discretizations of parabolic problems. IMA J. Numer. Anal. 39, 3 (2019), 1158–1179. Journal version, preprint PDF icon.

2018

34.   Ciarlet, Jr., P., and Vohralík, M. Localization of global norms and robust a posteriori error control for transmission problems with sign-changing coefficients. ESAIM Math. Model. Numer. Anal. 52, 5 (2018), 2037–2064. Journal version, preprint PDF icon.

35.   Cancčs, E., Dusson, G., Maday, Y., Stamm, B., and Vohralík, M. Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework. Numer. Math. 140, 4 (2018), 1033–1079. Journal version, preprint PDF icon.

36.   Daniel, P., Ern, A., Smears, I., and Vohralík, M. An adaptive hp-refinement strategy with computable guaranteed bound on the error reduction factor. Comput. Math. Appl. 76, 5 (2018), 967–983. Journal version, preprint PDF icon.

37.   Ali Hassan, S., Japhet, C., and Vohralík, M. A posteriori stopping criteria for space-time domain decomposition for the heat equation in mixed formulations. Electron. Trans. Numer. Anal. 49 (2018), 151–181. Journal version, preprint PDF icon.

38.   Ali Hassan, S., Japhet, C., Kern, M., and Vohralík, M. A posteriori stopping criteria for optimized Schwarz domain decomposition algorithms in mixed formulations. Comput. Methods Appl. Math. 18, 3 (2018), 495–519. Journal version, preprint PDF icon.

39.   Čermák, M., Hecht, F., Tang, Z., and Vohralík, M. Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem. Numer. Math. 138, 4 (2018), 1027–1065. Journal version, free view-only version, preprint PDF icon.

40.   Papež, J., Strakoš, Z., and Vohralík, M. Estimating and localizing the algebraic and total numerical errors using flux reconstructions. Numer. Math. 138, 3 (2018), 681–721. Journal version, free view-only version, preprint PDF icon.

41.   Vohralík, M., and Yousef, S. A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows. Comput. Methods Appl. Mech. Engrg. 331 (2018), 728–760. Journal version, preprint PDF icon.

2017

42.   Ern, A., Smears, I., and Vohralík, M. Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems. SIAM J. Numer. Anal. 55, 6 (2017), 2811–2834. Journal version, paper PDF icon.

43.   Cancčs, E., Dusson, G., Maday, Y., Stamm, B., and Vohralík, M. Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: conforming approximations. SIAM J. Numer. Anal. 55, 5 (2017), 2228–2254. Journal version, paper PDF icon.

44.   Ern, A., Smears, I., and Vohralík, M. Discrete p-robust H(div)-liftings and a posteriori estimates for elliptic problems with H-1 source terms. Calcolo 54, 3 (2017), 1009–1025. Journal version, free view-only version, preprint PDF icon.

2016

45.   Dolejší, V., Ern, A., and Vohralík, M. hp-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems. SIAM J. Sci. Comput. 38, 5 (2016), A3220–A3246. Journal version, paper PDF icon.

46.   Cancčs, E., Dusson, G., Maday, Y., Stamm, B., and Vohralík, M. A perturbation-method-based post-processing for the planewave discretization of Kohn–Sham models. J. Comput. Phys. 307 (2016), 446–459. Journal version, preprint PDF icon.

2015

47.   Ern, A., and Vohralík, M. Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations. SIAM J. Numer. Anal. 53, 2 (2015), 1058–1081. Journal version, paper PDF icon.

48.   Di Pietro, D. A., Vohralík, M., and Yousef, S. Adaptive regularization, linearization, and discretization and a posteriori error control for the two-phase Stefan problem. Math. Comp. 84, 291 (2015), 153–186. Journal version, preprint PDF icon.

2014

49.   Di Pietro, D. A., Vohralík, M., and Yousef, S. An a posteriori-based, fully adaptive algorithm with adaptive stopping criteria and mesh refinement for thermal multiphase compositional flows in porous media. Comput. Math. Appl. 68, 12 B (2014), 2331–2347. Journal version, preprint PDF icon.

50.   Cancčs, E., Dusson, G., Maday, Y., Stamm, B., and Vohralík, M. A perturbation-method-based a posteriori estimator for the planewave discretization of nonlinear Schrödinger equations. C. R. Math. Acad. Sci. Paris 352, 11 (2014), 941–946. Journal version, preprint PDF icon.

51.   Dolejší, V., Šebestová, I., and Vohralík, M. Algebraic and discretization error estimation by equilibrated fluxes for discontinuous Galerkin methods on nonmatching grids. J. Sci. Comput. 64, 1 (2015), 1–34. Journal version, preprint PDF icon.

52.   Di Pietro, D. A., Flauraud, E., Vohralík, M., and Yousef, S. A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media. J. Comput. Phys. 276 (2014), 163–187. Journal version, preprint PDF icon.

53.   Di Pietro, D. A., and Vohralík, M. A review of recent advances in discretization methods, a posteriori error analysis, and adaptive algorithms for numerical modeling in geosciences. Oil & Gas Science and Technology 69, 4 (2014), 701–729. Journal version, paper PDF icon.

54.   Cancčs, C., Pop, I. S., and Vohralík, M. An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow. Math. Comp. 83, 285 (2014), 153–188. Journal version, preprint PDF icon.

2013

55.   Vohralík, M., and Wheeler, M. F. A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows. Comput. Geosci. 17, 5 (2013), 789–812. Journal version, preprint PDF icon.

56.   Ern, A., and Vohralík, M. Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs. SIAM J. Sci. Comput. 35, 4 (2013), A1761–A1791. Journal version, paper PDF icon.

57.   Dolejší, V., Ern, A., and Vohralík, M. A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems. SIAM J. Numer. Anal. 51, 2 (2013), 773–793. Journal version, paper PDF icon.

58.   Pencheva, G. V., Vohralík, M., Wheeler, M. F., and Wildey, T. Robust a posteriori error control and adaptivity for multiscale, multinumerics, and mortar coupling. SIAM J. Numer. Anal. 51, 1 (2013), 526–554. Journal version, paper PDF icon.

59.   Ern, A., and Vohralík, M. Four closely related equilibrated flux reconstructions for nonconforming finite elements. C. R. Math. Acad. Sci. Paris 351, 1-2 (2013), 77–80. Journal version, preprint PDF icon.

60.   Ern, A., and Vohralík, M. Adaptive inexact Newton methods: a posteriori error control and speedup of calculations. SIAM News 46, 1 (2013), 1,4.

61.   Vohralík, M., and Wohlmuth, B. I. Mixed finite element methods: implementation with one unknown per element, local flux expressions, positivity, polygonal meshes, and relations to other methods. Math. Models Methods Appl. Sci. 23, 5 (2013), 803–838. Journal version, preprint PDF icon.

62.   Vohralík, M., and Wohlmuth, B. I. From face to element unknowns by local static condensation with application to nonconforming finite elements. Comput. Methods Appl. Mech. Engrg. 253 (2013), 517–529. Journal version, preprint PDF icon.

2012

63.   Hannukainen, A., Stenberg, R., and Vohralík, M. A unified framework for a posteriori error estimation for the Stokes problem. Numer. Math. 122, 4 (2012), 725–769. Journal version, preprint PDF icon.

64.   Ben Belgacem, F., Bernardi, C., Blouza, A., and Vohralík, M. On the unilateral contact between membranes. Part 2: A posteriori analysis and numerical experiments. IMA J. Numer. Anal. 32, 3 (2012), 1147–1172. Journal version, preprint PDF icon.

2011

65.   Hilhorst, D., and Vohralík, M. A posteriori error estimates for combined finite volume–finite element discretizations of reactive transport equations on nonmatching grids. Comput. Methods Appl. Mech. Engrg. 200, 5-8 (2011), 597–613. Journal version, preprint PDF icon.

66.   Vohralík, M. Guaranteed and fully robust a posteriori error estimates for conforming discretizations of diffusion problems with discontinuous coefficients. J. Sci. Comput. 46, 3 (2011), 397–438. Journal version, preprint PDF icon.

67.   El Alaoui, L., Ern, A., and Vohralík, M. Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems. Comput. Methods Appl. Mech. Engrg. 200, 37-40 (2011), 2782–2795. Journal version, preprint PDF icon.

2004–2010

68.   Jiránek, P., Strakoš, Z., and Vohralík, M. A posteriori error estimates including algebraic error and stopping criteria for iterative solvers. SIAM J. Sci. Comput. 32, 3 (2010), 1567–1590. Journal version, paper PDF icon.

69.   Vohralík, M. Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods. Math. Comp. 79, 272 (2010), 2001–2032. Journal version, preprint PDF icon.

70.   Ern, A., and Vohralík, M. A posteriori error estimation based on potential and flux reconstruction for the heat equation. SIAM J. Numer. Anal. 48, 1 (2010), 198–223. Journal version, paper PDF icon.

71.   Ern, A., Stephansen, A. F., and Vohralík, M. Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems. J. Comput. Appl. Math. 234, 1 (2010), 114–130. Journal version, preprint PDF icon.

72.   Eymard, R., Hilhorst, D., and Vohralík, M. A combined finite volume–finite element scheme for the discretization of strongly nonlinear convection–diffusion–reaction problems on nonmatching grids. Numer. Methods Partial Differential Equations 26, 3 (2010), 612–646. Journal version, preprint PDF icon.

73.   Cheddadi, I., Fučík, R., Prieto, M. I., and Vohralík, M. Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems. M2AN Math. Model. Numer. Anal. 43, 5 (2009), 867–888. Journal version, preprint PDF icon.

74.   Ern, A., and Vohralík, M. Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids. C. R. Math. Acad. Sci. Paris 347, 7-8 (2009), 441–444. Journal version, preprint PDF icon.

75.   Ben Belgacem, F., Bernardi, C., Blouza, A., and Vohralík, M. On the unilateral contact between membranes. Part 1: Finite element discretization and mixed reformulation. Math. Model. Nat. Phenom. 4, 1 (2009), 21–43. Journal version, preprint PDF icon.

76.   Ben Belgacem, F., Bernardi, C., Blouza, A., and Vohralík, M. A finite element discretization of the contact between two membranes. M2AN Math. Model. Numer. Anal. 43, 1 (2009), 33–52. Journal version, preprint PDF icon.

77.   Vohralík, M. Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods. Numer. Math. 111, 1 (2008), 121–158. Journal version, preprint PDF icon.

78.   Vohralík, M. A posteriori error estimation in the conforming finite element method based on its local conservativity and using local minimization. C. R. Math. Acad. Sci. Paris 346, 11-12 (2008), 687–690. Journal version, preprint PDF icon.

79.   Ern, A., Nicaise, S., and Vohralík, M. An accurate H(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems. C. R. Math. Acad. Sci. Paris 345, 12 (2007), 709–712. Journal version, preprint PDF icon.

80.   Vohralík, M. A posteriori error estimates for lowest-order mixed finite element discretizations of convection-diffusion-reaction equations. SIAM J. Numer. Anal. 45, 4 (2007), 1570–1599. Journal version, paper PDF icon.

81.   Vohralík, M., Maryška, J., and Severýn, O. Mixed and nonconforming finite element methods on a system of polygons. Appl. Numer. Math. 57, 2 (2007), 176–193. Journal version, preprint PDF icon.

82.   Eymard, R., Hilhorst, D., and Vohralík, M. A combined finite volume–nonconforming/mixed-hybrid finite element scheme for degenerate parabolic problems. Numer. Math. 105, 1 (2006), 73–131. Journal version, preprint PDF icon.

83.   Vohralík, M. Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes. M2AN Math. Model. Numer. Anal. 40, 2 (2006), 367–391. Journal version, preprint PDF icon.

84.   Vohralík, M. On the discrete Poincaré–Friedrichs inequalities for nonconforming approximations of the Sobolev space H1. Numer. Funct. Anal. Optim. 26, 7-8 (2005), 925–952. Journal version, preprint PDF icon.

85.   Vohralík, M. Equivalence between mixed finite element and multi-point finite volume methods. C. R. Math. Acad. Sci. Paris 339, 7 (2004), 525–528. Journal version, preprint PDF icon.

86.   Maryška, J., Severýn, O., and Vohralík, M. Numerical simulation of fracture flow with a mixed-hybrid FEM stochastic discrete fracture network model. Comput. Geosci. 8, 3 (2004), 217–234. Journal version, preprint PDF icon.

Papers submitted

87.   Demkowicz, L., and Vohralík, M. p-robust equivalence of global continuous constrained and local discontinuous unconstrained approximation, a p-stable local commuting projector, and optimal elementwise hp approximation estimates in H(div). HAL Preprint 04503603, submitted for publication, 2024. PDF icon.

88.   Vohralík, M. p-robust equivalence of global continuous and local discontinuous approximation, a p-stable local projector, and optimal elementwise hp approximation estimates in H1. HAL Preprint 04436063, submitted for publication, 2024. PDF icon.

89.   Buffa, A., Chanon, O., Grappein, D., Vázquez, R., and Vohralík, M. An equilibrated flux a posteriori error estimator for defeaturing problems. HAL Preprint 04379236, submitted for publication, 2023. PDF icon.

90.   Chaumont-Frelet, T., and Vohralík, M. A stable local commuting projector and optimal hp approximation estimates in H(curl). HAL Preprint 03817302, submitted for publication, 2023. PDF icon.

91.   Harnist, A., Mitra, K., Rappaport, A., and Vohralík, M. Robust energy a posteriori estimates for nonlinear elliptic problems. HAL Preprint 04033438, 2023. PDF icon.

92.   Févotte, F., Rappaport, A., and Vohralík, M. Adaptive regularization for the Richards equation. HAL Preprint 04266827, submitted for publication, 2023. PDF icon.

93.   Mitra, K., and Vohralík, M. Guaranteed, locally efficient, and robust a posteriori estimates for nonlinear elliptic problems in iteration-dependent norms. An orthogonal decomposition result based on iterative linearization. HAL Preprint 04156711, submitted for publication, 2023. PDF icon.

94.   Chaumont-Frelet, T., and Vohralík, M. Constrained and unconstrained stable discrete minimizations for p-robust local reconstructions in vertex patches in the de Rham complex. HAL Preprint 03749682, submitted for publication, 2023. PDF icon.