An adaptive method for linear parabolic differential equations. (English) Zbl 0637.65118

Using the Euler backward formula, a one-dimensional parabolic equation is first discretized in the spirit of Rothe. The resulting elliptic equation is then approximated using linear elements. The error of the Rothe step is estimated by measuring the defect of the solution inserted into the Crank-Nicolson formula, the error of the spatial discretization by inserting the solution into a finer discretization. On this basis, applying the principle of equidistributing the defects, time steps and spatial steps are chosen (independently from each other) in an adaptive manner. A numerical example illustrates the adequateness of the proposed step selection algorithm. For a considerable part of the theoretical background the author refers to his thesis.
Reviewer: G.Stoyan


65N40 Method of lines for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
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