×

Design and convergence analysis for an adaptive discretization of the heat equation. (English) Zbl 1261.65092

The authors derive an algorithm for the adaptive approximation of solutions to parabolic equations. It is based on adaptive finite elements in space and the implicit Euler discretization in time with adaptive time-step sizes. The authors also prove that, given a positive tolerance for the error, the adaptive algorithm reaches the final time with a space-time error between the continuous and the discrete solution that is below the given tolerance.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs

Software:

ALBERTA; ALBERT
PDF BibTeX XML Cite
Full Text: DOI