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HP-finite element approximationson non-matching gridsfor 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. [email protected].
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Abstract

We propose and analyze a domain decomposition method on non-matching gridsfor partial differential equations with non-negativecharacteristic form. No weak or strong continuity of the finiteelement functions, their normal derivatives, or linearcombinations of the two is imposed across the boundaries of the subdomains.Instead, we employ suitable bilinear forms defined on the commoninterfaces, typical of discontinuous Galerkinapproximations.We prove an error bound which is optimal with respect to the mesh–size andsuboptimal with respect to the polynomial degree.Our analysis is valid for arbitrary shape–regular meshes and arbitrarypartitions 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-dimensionalnumerical 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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