A Space-time Adaptive Semi Dual Weighted Residual Finite Element Method

We propose in this paper a space-time adaptive algorithm based on the Dual Weighted Residual (DWR) idea in the framework of finite element method. Our algorithm consists of applying the DWR technique locally in each time interval In := (tn−1, tn], 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 criterium that allows us to have control of the time step ∆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 meshed made of simplices.