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TWO-SCALE PRODUCT APPROXIMATION FOR SEMILINEAR PARABOLIC PROBLEMS IN MIXED METHODS

서보윤|박은재|김동호
대한수학회 (The Korean Mathematical Society)|2014.03|대한수학회지 (Journal of the KMS)|제51권 제2호|pp. 267-288

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참고문헌

키워드

mixed finite element methodtwo-scale gridproduct approximationinterpolation of coeffi- cientssemilinear parabolic problem.
주제분류수학

초록

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 rele- vant variables. Numerical results are presented to support the theory developed in this paper.

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 rele- vant variables. Numerical results are presented to support the theory developed in this paper.

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