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

Chou, S. H.; Li, Q.

doi:10.1090/S0025-5718-1990-1011439-X

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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