Convergence of the nonconforming Wilson element for a class of nonlinear parabolic problems-Reference-Cited by-同舟云学术

Convergence of the nonconforming Wilson element for a class of nonlinear parabolic problems

Published:1990 Issue:190 Volume:54 Page:509-524
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Chou S. H.,Li Q.

Abstract

This paper deals with the convergence properties of the nonconforming quadrilateral Wilson element for a class of nonlinear parabolic problems in two space dimensions. Optimal H 1 {H^1} and L 2 {L_2} error estimates for the continuous time Galerkin approximations are derived. It is also shown for rectangular meshes that the gradient of the Wilson element solution possesses superconvergence, and that the L ∞ {L_\infty } error on the gradient is of order h log ⁡ ( 1 / h ) h\log (1/h) .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1990-54-190/S0025-5718-1990-1011439-X/S0025-5718-1990-1011439-X.pdf

Reference6 articles.

1. Galerkin methods for parabolic equations;Douglas, Jim, Jr.;SIAM J. Numer. Anal.,1970

2. Convergence of the nonconforming Wilson element for arbitrary quadrilateral meshes;Lesaint, P.;Numer. Math.,1980

3. A convergence condition for the quadrilateral Wilson element;Shi, Zhong Ci;Numer. Math.,1984

4. 𝐿_{∞}-convergence of nonconforming finite element approximations;Shen, Shu Min;Math. Numer. Sinica,1986

5. H. Wang, Superconvergence of the Wilson element, J. Shandong Univ. 21 (1986), 89-95.

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