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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 37.1 (2010): 91-115. <http://eudml.org/doc/194158>.

@article{Toselli2010,

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},

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

language = {eng},

month = {3},

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/194158},

volume = {37},

year = {2010},

}

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

DA - 2010/3//

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; domain decomposition; discontinuous Galerkin method; hp-finite elements; error bounds; numerical results

UR - http://eudml.org/doc/194158

ER -

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