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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: 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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DOI: https://doi.org/10.1090/S0025-5718-1990-1011439-X
Keywords: Parabolic equation, Wilson element
Article copyright: © Copyright 1990 American Mathematical Society