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Parabolic finite element equations in nonconvex polygonal domains. (English) Zbl 1108.65097
The object of this paper is to show that certain known error estimates for piecewise linear finite element approximations to solution of elliptic equations in nonconvex polygonal domains [cf. A. H. Schatz and L. B. Wahlbin, Math. Comput. 33, 465–492 (1979; Zbl 0417.65053)] carry over to parabolic problems. Nonsmooth data estimate for the homogeneous heat equation and a discussion of mesh refinement in the context of the parabolic equation are given. Some examples of error bounds for fully discrete methods obtained by discretization in time by finite differences of the spatially semidiscrete parabolic equation are also given.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M20 Method of lines 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
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
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