A Discrete Duality Finite Volume Approach to Hodge Decomposition and div‐curl Problems on Almost Arbitrary Two‐Dimensional Meshes

DOI10.1137/060655031zbMath1152.65110OpenAlexW2036663341MaRDI QIDQ3507507

Sarah Delcourte, Komla Domelevo, Pascal Omnes

Publication date: 19 June 2008

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/060655031

zbMATH Keywords

convergenceerror estimatesdiscrete differential operatorsnonconforming meshesdiv-curl equationsdiscrete duality finite volume methodarbitrary meshesdegenerating meshesdiscrete Green formuladiscrete Hodge decomposition

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) PDEs in connection with optics and electromagnetic theory (35Q60) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Electro- and magnetostatics (78A30)

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