Some remarks on the behaviour of the finite element solution in nonsmooth domains

Mitsuhiro T. Nakao; Takehiko Kinoshita

doi:10.1016/j.aml.2007.11.005

Some remarks on the behaviour of the finite element solution in nonsmooth domains

Mitsuhiro T. Nakao, Takehiko Kinoshita

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

In this work, we consider the behaviour of the residual error using a smooth finite element solution for elliptic problems on nonconvex and nonsmooth domains. It is proved that, against expectations, the residual error is unbounded and actually diverges to infinity as the mesh size goes to zero. A numerical example which illustrates this phenomenon will be presented for the Poisson equation on an L-shaped domain using a C¹ Hermite element, and similar results will be shown for a C⁰ element with a posteriori smoothing.

Original language	English
Pages (from-to)	1310-1314
Number of pages	5
Journal	Applied Mathematics Letters
Volume	21
Issue number	12
DOIs	https://doi.org/10.1016/j.aml.2007.11.005
Publication status	Published - 2008 Dec
Externally published	Yes

Keywords

Nonsmooth domain
Poisson equation
Residual error

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aml.2007.11.005

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AB - In this work, we consider the behaviour of the residual error using a smooth finite element solution for elliptic problems on nonconvex and nonsmooth domains. It is proved that, against expectations, the residual error is unbounded and actually diverges to infinity as the mesh size goes to zero. A numerical example which illustrates this phenomenon will be presented for the Poisson equation on an L-shaped domain using a C1 Hermite element, and similar results will be shown for a C0 element with a posteriori smoothing.

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