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A space-time adaptive semi dual weighted residual finite element method. (English) Zbl 1242.65200

Summary: We propose in this paper a space-time adaptive algorithm based on the Dual Weighted Residual (DWR) idea in the framework of the finite element method. Our algorithm consists of applying the DWR technique locally in each time interval \(I_n:=(t_{n-1},t_n]\); thus, we control the local or truncation error for a functional of the solution \(J(u)\). That means that we can define a self-sufficient criterion that allows us to have control of the time step \(\Delta t\) and the mesh size \(h\) as time progresses. Another good feature of our algorithm is the extension of the spatial post-processing procedure of the traditional DWR method to unstructured meshes made of simplices.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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