# $HP$-finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form

- Volume: 37, Issue: 1, page 91-115
- ISSN: 0764-583X

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topToselli, Andrea. "${HP}$-finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.1 (2003): 91-115. <http://eudml.org/doc/244912>.

@article{Toselli2003,

abstract = {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.},

author = {Toselli, Andrea},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {Advection–diffusion; hyperbolic problems; stabilization; domain decomposition; non-matching grids; discontinuous Galerkin; $hp$-finite elements; Advection-diffusion equation; discontinuous Galerkin method; hp-finite elements; error bounds; numerical results},

language = {eng},

number = {1},

pages = {91-115},

publisher = {EDP-Sciences},

title = {$\{HP\}$-finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form},

url = {http://eudml.org/doc/244912},

volume = {37},

year = {2003},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2003

PB - EDP-Sciences

VL - 37

IS - 1

SP - 91

EP - 115

AB - 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.

LA - eng

KW - Advection–diffusion; hyperbolic problems; stabilization; domain decomposition; non-matching grids; discontinuous Galerkin; $hp$-finite elements; Advection-diffusion equation; discontinuous Galerkin method; hp-finite elements; error bounds; numerical results

UR - http://eudml.org/doc/244912

ER -

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