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

martin.vohralik@inria.fr

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.

Plus dans la galerie GATIPOR Více v galerii GATIPOR More in the GATIPOR gallery

Thésards Doktorandi Ph.D. students

Nicolas Hugot (2023–)
Clément Maradei (2023–)
Daniel Zegarra Vasquez (2021–)
Ari Rappaport (2021–2024)
Morgane Steins (2020–2023)
Joëlle Ferzly (2019–2022)
Ani Miraçi (2017–2020)
Jad Dabaghi (2015–2019)
Patrik Daniel (2015–2019)
Sarah Ali Hassan (2013–2017)
Soleiman Yousef (2009–2013)
Carole Heinry (2009–2013)
Nancy Chalhoub (2008–2012)

Post-docs Post-doktorandi Post-docs

Akram Beni Hamad (2022–)
André Harnist (2021–2023)
Manuela Bastidas Olivares (2021–2022)
Koondanibha Mitra (2020–2021)
Kenan Kergrene (2018–2020)
Jan Papež (2019)
Mohammad Zakerzadeh (2017–2019)
Gouranga Mallik (2017–2018)
Iain Smears (2015–2017)
Zuqi Tang (2013–2015)

Equipe SERENA Projekt SERENA SERENA team

Liens académiques Akademické odkazy Academic links

Laboratoire Jacques-Louis Lions, Sorbonne Université, Paris
Center for Subsurface Modeling, Université de Texas à Austin
Analyse numérique, Université Charles, Prague
Faculté nucléaire, Université Technique Tchèque à Prague Laboratoř Jacques-Louise Lionse, Univerzita Sorbonne, Paříž
Center for Subsurface Modeling, Texaská Univerzita v Austinu
Numerická analýza, Univerzita Karlova, Praha
Fakulta jaderná a fyzikálně inženýrská, ČVUT v Praze Laboratoire Jacques-Louis Lions, Sorbonne University, Paris
Center for Subsurface Modeling, University of Texas at Austin
Numerical analysis, Charles University, Prague
Nuclear Faculty, Czech Technical University in Prague

Liens industriels Industriální odkazy Industrial links

IFP Energies Nouvelles
Agence nationale pour la gestion des déchets radioactifs IFP Energies Nouvelles
Francouzská agentura pro ukládání jaderných odpadů IFP Energies Nouvelles
French National Radioactive Waste Management Agency