On the L2 a Priori error estimates to the finite element solution of elliptic problems with singular adjoint operator

T. Kinoshita, K. Hashimoto, M. T. Nakao

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The Aubin-Nitsche trick for the finite element method of Dirichlet boundary value problem is a well-known technique to obtain a higher order a priori L2 error estimation than that of [image omitted] estimates by considering the regularly dual problem. However, as far as the authors determine, when the dual problem is singular, it was not known at all up to now whether the a priori order of L2 error is still higher than that of [image omitted] error. In this paper, we propose a technique for getting a priori L2 error estimation by some verified numerical computations for the finite element projection. This enables us to obtain a higher order L2 a priori error than that of [image omitted] error, even though the associated dual problem is singular. Note that our results are not a posteriori estimates but the determination of a priori constants.

Original languageEnglish
Pages (from-to)289-305
Number of pages17
JournalNumerical Functional Analysis and Optimization
Volume30
Issue number3-4
DOIs
Publication statusPublished - 2009 Mar
Externally publishedYes

Fingerprint

Adjoint Operator
A Priori Error Estimates
Finite Element Solution
Elliptic Problems
Mathematical operators
Dual Problem
Error Estimation
Error analysis
Higher Order
A Posteriori Estimates
Dirichlet Boundary Value Problem
Numerical Computation
Boundary value problems
Finite Element Method
Projection
Finite Element
Finite element method
Estimate

Keywords

  • A priori error estimates
  • FEM
  • Noncoercive elliptic problems

ASJC Scopus subject areas

  • Analysis
  • Control and Optimization
  • Signal Processing
  • Computer Science Applications

Cite this

On the L2 a Priori error estimates to the finite element solution of elliptic problems with singular adjoint operator. / Kinoshita, T.; Hashimoto, K.; Nakao, M. T.

In: Numerical Functional Analysis and Optimization, Vol. 30, No. 3-4, 03.2009, p. 289-305.

Research output: Contribution to journalArticle

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