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Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 07/2019, Volume 42, Issue 11, pp. 4008 - 4016
This short note reports a lowest order divergence‐free Stokes element on quadrilateral meshes. The velocity space is based on a P1 spline element over the... 
divergence‐free | stokes element | fluid mechanics | quadrilateral | finite elements | MATHEMATICS, APPLIED | FINITE-ELEMENTS | divergence-free | Quadrilaterals | Subspace methods | Divergence
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 2004, Volume 194, Issue 2, pp. 588 - 610
In this paper, we develop the locally divergence-free discontinuous Galerkin method for numerically solving the Maxwell equations. The distinctive feature of... 
Divergence-free solutions | Discontinuous Galerkin method | Maxwell equations | Divergence-free | FIELDS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | discontinuous Galerkin method | SYSTEMS | divergence-free solutions | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | FINITE-ELEMENT-METHOD
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 12/2019
Journal Article
International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 01/2019, Volume 89, Issue 1-2, pp. 16 - 42
Journal Article
Communications in Computational Physics, ISSN 1815-2406, 02/2017, Volume 21, Issue 2, pp. 423 - 442
In this paper we consider a discontinuous Galerkin discretization of the ideal magnetohydrodynamics (MHD) equations on unstructured meshes, and the divergence... 
Ideal magnetohydrodynamics equations | divergence free constraint | divergence free cleaning technique | discontinuous Galerkin method | locally divergence free projection | IDEAL MHD EQUATIONS | FRAMEWORK | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | FINITE-ELEMENT-METHOD | SCHEMES
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 01/2018, Volume 75, Issue 1, pp. 199 - 217
We propose a new method for analyzing the limit (safe) load of elastoplastic media governed by the Hencky plasticity law and deduce fully computable bounds of... 
Divergence free fields | Hencky’s plasticity | Computable bounds | Penalization | Limit load
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 04/2014, Volume 263, pp. 206 - 221
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 10/2019, Volume 113, Issue 4, pp. 443 - 448
Journal Article
Mathematics and Computers in Simulation, ISSN 0378-4754, 04/2020, Volume 170, pp. 51 - 78
The performance of different classic or more recent finite element formulations for Stokes, coupled Stokes–Darcy and Brinkman problems is discussed.... 
Coupled Stokes–Darcy flow | Discontinuous Galerkin | Mixed finite elements methods | Divergence-free simulation | Stokes flow
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 03/2019, Volume 88, Issue 316, pp. 553 - 581
We develop a class of mixed finite element schemes for stationary magnetohydrodynamics (MHD) models, using the magnetic field \bm B and the current density \bm... 
Divergence-free | MHD equations | Stationary | Finite element | MATHEMATICS, APPLIED | CONSERVATIVE SCHEME | stationary | finite element | EXTERIOR CALCULUS | FLOWS
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 04/2020, Volume 368, p. 112479
This paper presents a lowest-order weak Galerkin (WG) finite element method for solving the Stokes equations on convex polygonal meshes. Constant vectors are... 
Discretely divergence-free | Polygonal meshes | Weak Galerkin | Lowest-order finite elements | Stokes flow | MATHEMATICS, APPLIED | DISCONTINUOUS GALERKIN
Journal Article
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 07/2019, Volume 127, pp. 67 - 88
We extend our analysis of divergence-free positive symmetric tensors (DPT) begun in a previous paper. On the one hand, we refine the statements and give more... 
Divergence-free tensors | Maxwell's equations | Integrability | Determinant | Vlasov–Poisson equation | Vlasov-Poisson equation | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
ESAIM: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 03/2017, Volume 51, Issue 2, pp. 509 - 535
Journal Article