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A PRIORI L² ERROR ANALYSIS FOR AN EXPANDED MIXED FINITE ELEMENT METHOD FOR QUASILINEAR PSEUDO-PARABOLIC EQUATIONS

이현영|신준용|엄미례
대한수학회 (The Korean Mathematical Society)|2014.01|대한수학회지 (Journal of the KMS)|제51권 제1호|pp. 67-86

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참고문헌

키워드

semidiscrete approximationspseudo-parabolic equationan expanded mixed finite element methodL² optimal convergence.
주제분류수학

초록

Based on an expanded mixed finite element method, we con- sider the semidiscrete approximations of the solution u of the quasilinear pseudo-parabolic equation defined on Ω ⊂ R d , 1 ≤ d ≤ 3. We construct the semidiscrete approximations of ∇u and a(u)∇u + b(u)∇u t as well as u and prove the existence of the semidiscrete approximations. And also we prove the optimal convergence of ∇u and a(u)∇u + b(u)∇u t as well as u in L² normed space.

Abstract

Based on an expanded mixed finite element method, we con- sider the semidiscrete approximations of the solution u of the quasilinear pseudo-parabolic equation defined on Ω ⊂ R d , 1 ≤ d ≤ 3. We construct the semidiscrete approximations of ∇u and a(u)∇u + b(u)∇u t as well as u and prove the existence of the semidiscrete approximations. And also we prove the optimal convergence of ∇u and a(u)∇u + b(u)∇u t as well as u in L² normed space.

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