Graded mesh approximation in weighted sobolev spaces and elliptic equations in 2D

James H. Adler, Victor Nistor

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We study the approximation properties of some general finiteelement spaces constructed using improved graded meshes. In our results, either the approximating function or the function to be approximated (or both) are in a weighted Sobolev space. We consider also the Lp-version of these spaces. The finite-element spaces that we define are obtained from conformally invariant families of finite elements (no affine invariance is used), stressing the use of elements that lead to higher regularity finite-element spaces. We prove that for a suitable grading of the meshes, one obtains the usual optimal approximation results. We provide a construction of these spaces that does not lead to long, "skinny" triangles. Our results are then used to obtain L2-error estimates and hm-quasi-optimal rates of convergence for the FEM approximation of solutions of strongly elliptic interface/boundary value problems.

Original languageEnglish (US)
Pages (from-to)2191-2220
Number of pages30
JournalMathematics of Computation
Volume84
Issue number295
DOIs
StatePublished - Jan 1 2015

Fingerprint

Graded Meshes
Sobolev spaces
Weighted Sobolev Spaces
Elliptic Equations
Finite Element
Approximation
Invariance
Boundary value problems
Interfaces (computer)
Finite element method
Affine Invariance
Optimal Approximation
Optimal Rate of Convergence
Grading
Approximation Property
Error Estimates
Triangle
Regularity
Boundary Value Problem
Mesh

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

Cite this

Adler, James H. ; Nistor, Victor. / Graded mesh approximation in weighted sobolev spaces and elliptic equations in 2D. In: Mathematics of Computation. 2015 ; Vol. 84, No. 295. pp. 2191-2220.
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Graded mesh approximation in weighted sobolev spaces and elliptic equations in 2D. / Adler, James H.; Nistor, Victor.

In: Mathematics of Computation, Vol. 84, No. 295, 01.01.2015, p. 2191-2220.

Research output: Contribution to journalArticle

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