Superconvergence of Recovered Gradients of Discrete Time/Piecewise Linear Galerkin Approximations for Linear and Nonlinear Parabolic Problems
RICE UNIV HOUSTON TX DEPT OF MATHEMATICAL SCIENCES
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Superconvergent error estimates in e2H1 and einfinityH1 norms are derived for recovered gradients of finite difference in timepiecewise linear Galerkin approximations in space for linear and quasi-nonlinear parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the parabolic context, and covers problems in regions with non-smooth boundaries under certain assumptions on the regularity of the solutions.
- Numerical Mathematics