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A nonconforming scheme to solve the parabolic problem. (English) Zbl 1410.65380

Summary: The convergence order \(O(h^{2})\) of the Wilson nonconforming element has been derived by the superconvergence methods so far. In this paper, a nonconforming semi-discrete scheme is derived by the discontinuous Galerkin method when using the Wilson element approximation of the parabolic problem. In the new scheme, the penalty parameter is accurately estimated and the consistency error vanishes. Therefore, the error estimate can only be determined by the interpolation error of which the convergence order is \(O(h^{2})\).

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
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