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We propose and analyze a domain decomposition method on non-matching grids for partial differential equations with non-negative characteristic form. No weak or strong continuity of the finite element functions, their normal derivatives, or linear combinations of the two is imposed across the boundaries of the subdomains. Instead, we employ suitable bilinear forms defined on the common interfaces, typical of discontinuous Galerkin approximations. We prove an error bound which is optimal with respect to the mesh-size and suboptimal with respect to the polynomial degree. Our analysis is valid for arbitrary shape-regular meshes and arbitrary partitions into subdomains. Our method can be applied to advective, diffusive, and mixed-type equations, as well, and is well-suited for problems coupling hyperbolic and elliptic equations. We present some two-dimensional numerical results that support our analysis for the case of linear finite elements.
Mots-clés : Advection-diffusion, hyperbolic problems, stabilization, domain decomposition, non-matching grids, discontinuous Galerkin, $hp$-finite elements
@article{M2AN_2003__37_1_91_0,
author = {Toselli, Andrea},
title = {${HP}$-finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {91--115},
publisher = {EDP-Sciences},
volume = {37},
number = {1},
year = {2003},
doi = {10.1051/m2an:2003018},
zbl = {1028.65124},
mrnumber = {1972652},
language = {en},
url = {https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003018/}
}
TY - JOUR
AU - Toselli, Andrea
TI - ${HP}$-finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form
JO - ESAIM: Mathematical Modelling and Numerical Analysis
PY - 2003
SP - 91
EP - 115
VL - 37
IS - 1
PB - EDP-Sciences
UR - https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003018/
DO - 10.1051/m2an:2003018
LA - en
ID - M2AN_2003__37_1_91_0
ER -
%0 Journal Article
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%T ${HP}$-finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form
%J ESAIM: Mathematical Modelling and Numerical Analysis
%D 2003
%P 91-115
%V 37
%N 1
%I EDP-Sciences
%U https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003018/
%R 10.1051/m2an:2003018
%G en
%F M2AN_2003__37_1_91_0
Toselli, Andrea. ${HP}$-finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 1, pp. 91-115. doi : 10.1051/m2an:2003018. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003018/
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