Martin Vohralík

Directeur de recherche Inria Vědecký pracovník, Inria Senior researcher at Inria

Equipe-projet SERENA, responsable Projekt SERENA, vedoucí Project-team SERENA, team leader

Localisation des normes W^-1,q et de distance Lokalizace W^-1,q a vzdálenostní normy Localization of the W^-1,q and distance norms

• dual norm of any bounded linear functional on the Sobolev space W₀^1,p localizes under an orthogonality condition: equals the l^q sum of local contributions;
• estimates taking into account the violation of the orthogonality condition;
• distance to the Sobolev space H₀¹ localizes: equals the l² sum of local contributions (no orthogonality condition);
• implies local efficiency and robustness of a posteriori estimates for nonlinear and non-coercive partial differential equations in divergence form;
• includes the case of inexact solvers;
• H₀¹ setting including nonconformity: paper with Patrick Ciarlet, Jr., presentation;
• W₀^1,p setting: paper with Jan Blechta and Josef Málek, presentation.

Equivalence local–global, projection et approximation hp dans H(div) Lokální – globální ekvivalence, projekce a hp aproximace v H(div) Local–global equivalence, projection, and hp approximation in H(div)

• global-best approximation (constraints on normal component continuity and divergence) is equivalent to the sum of independent local-best approximations (no constraints);
• gives rise to a simple stable local commuting projector in H(div);
• this projector delivers approximation error equivalent to the local-best approximation;
• leads to optimal hp approximation estimates in H(div);
• applies under the minimal necessary Sobolev regularity;
• gives optimal a priori hp-error estimates for mixed and least-squares finite element methods;
• paper with Alexandre Ern, Thirupathi Gudi, and Iain Smears, presentation.

Maillages polytopaux et écoulements complexes en milieux poreux Polytopální sítě a komplexní proudění v porézním prostředí Polytopal meshes and complex porous media flows

• general polytopal meshes;
• easy-to-implement and fast-to-run a posteriori error estimates given by a simple matrix–vector multiplication;
• works for any lowest-order locally conservative method, extends to higher-order;
• guaranteed upper bound on the total error;
• distinction of different error components (spatial discretization, temporal discretization, linearization, algebraic solver);
• unsteady nonlinear coupled degenerate problems (multiphase multicomponent flows in porous media);
• paper with Soleiman Yousef, presentation.

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Thésards Doktorandi Ph.D. students

Post-docs Post-doktorandi Post-docs

Equipe SERENA Projekt SERENA SERENA team

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