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HP-finite element approximationson non-matching grids for partial differential equations with non-negativecharacteristic form

Published online by Cambridge University Press:  15 March 2003

Andrea Toselli
Andrea Toselli*
Affiliation:
Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland. toselli@sam.math.ethz.ch.
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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.

Keywords

Advection–diffusionhyperbolic problemsstabilizationdomain decompositionnon-matching gridsdiscontinuous Galerkinhp-finite elements.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 1 , January 2003 , pp. 91 - 115
Copyright
© EDP Sciences, SMAI, 2003

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