A constructive a priori error estimation for finite element discretizations in a non-convex domain using singular functions | Zendy

Kenta Kobayashi | Zendy

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A constructive a priori error estimation for finite element discretizations in a non-convex domain using singular functions

Author(s) -

Kenta Kobayashi

Publication year - 2009

Publication title -

japan journal of industrial and applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.356

H-Index - 28

eISSN - 1868-937X

pISSN - 0916-7005

DOI - 10.1007/bf03186546

Subject(s) - finite element method , mathematics , bounded function , domain (mathematical analysis) , poisson's equation , a priori and a posteriori , mathematical analysis , rate of convergence , convergence (economics) , constructive , function (biology) , basis function , computer science , computer network , philosophy , channel (broadcasting) , physics , epistemology , process (computing) , evolutionary biology , biology , economics , thermodynamics , economic growth , operating system

In solving elliptic problems by the finite element method in a bounded domain which has a re-entrant corner, the rate of convergence can be improved by adding a singular function to the usual interpolating basis. When the domain is enclosed by line segments which form a corner of π/2 or 3π/2, we have obtained an explicit a prioriH 01 error estimation ofO(h) and anL 2 error estimation ofO(h 2) for such a finite element solution of the Poisson equation. Particularly, we emphasize that all constants in our error estimates are numerically determined, which plays an essential role in the numerical verification of solutions to non-linear elliptic problems.

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