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Convergence analysis of finite element method for a parabolic obstacle problem. (English) Zbl 1418.65173

Summary: A conforming finite element method is proposed and analyzed for numerical approximation of the solution of a parabolic variational inequality of the obstacle problem. The model problem, which is originally proposed using a general obstacle, is reframed as a model problem with zero obstacle but with non-homogeneous Dirichlet boundary conditions. Subsequently the discrete problem is reframed and the error analysis proving the convergence of the method is performed. The analysis requires a positive preserving interpolation with non-homogeneous Dirichlet boundary condition and a post-processed solution that satisfies the boundary conditions sharply. The results in the article extend the results of C. Johnson [SIAM J. Numer. Anal. 13, 599–606 (1976; Zbl 0337.65055)] for a zero obstacle function to a more general obstacle function.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs

Citations:

Zbl 0337.65055
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References:

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