Convergence of the nonconforming Wilson element for a class of nonlinear parabolic problems
Authors:
S. H. Chou and Q. Li
Journal:
Math. Comp. 54 (1990), 509-524
MSC:
Primary 65N30
DOI:
https://doi.org/10.1090/S0025-5718-1990-1011439-X
MathSciNet review:
1011439
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Abstract | References | Similar Articles | Additional Information
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 ${H^1}$ and ${L_2}$ 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 ${L_\infty }$ error on the gradient is of order $h\log (1/h)$.
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Keywords:
Parabolic equation,
Wilson element
Article copyright:
© Copyright 1990
American Mathematical Society