Two-scale product approximation for semilinear parabolic problems in mixed methods

Dongho Kim, Eun-Jae Park, Boyoon Seo

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We propose and analyze two-scale product approximation for semilinear heat equations in the mixed finite element method. In order to efficiently resolve nonlinear algebraic equations resulting from the mixed method for semilinear parabolic problems, we treat the nonlinear terms using some interpolation operator and exploit a two-scale grid algorithm. With this scheme, the nonlinear problem is reduced to a linear problem on a fine scale mesh without losing overall accuracy of the final system. We derive optimal order L((0, T];L2(Ω))-error estimates for the relevant variables. Numerical results are presented to support the theory developed in this paper.

Original languageEnglish
Pages (from-to)267-288
Number of pages22
JournalJournal of the Korean Mathematical Society
Volume51
Issue number2
DOIs
Publication statusPublished - 2014 Mar 10

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Semilinear Parabolic Problem
Mixed Methods
Approximation
Semilinear Heat Equation
Nonlinear Algebraic Equations
Mixed Finite Element Method
Nonlinear Problem
Error Estimates
Resolve
Interpolate
Mesh
Grid
Numerical Results
Term
Operator

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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abstract = "We propose and analyze two-scale product approximation for semilinear heat equations in the mixed finite element method. In order to efficiently resolve nonlinear algebraic equations resulting from the mixed method for semilinear parabolic problems, we treat the nonlinear terms using some interpolation operator and exploit a two-scale grid algorithm. With this scheme, the nonlinear problem is reduced to a linear problem on a fine scale mesh without losing overall accuracy of the final system. We derive optimal order L∞((0, T];L2(Ω))-error estimates for the relevant variables. Numerical results are presented to support the theory developed in this paper.",
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Two-scale product approximation for semilinear parabolic problems in mixed methods. / Kim, Dongho; Park, Eun-Jae; Seo, Boyoon.

In: Journal of the Korean Mathematical Society, Vol. 51, No. 2, 10.03.2014, p. 267-288.

Research output: Contribution to journalArticle

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