Ornela Mulita (SISSA)
Wednesday, November 13, 2019 - 11:15
Humboldt-Universität, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin, Raum 2.417, Haus 2
Forschungsseminar "Numerische Mathematik"
Prof. C. Carstensen
We propose a new algorithm for Adaptive Finite Element Methods based on Smoothing iterations (S-AFEM). The algorithm is inspired by the ascending phase of the V-cycle multigrid method: we replace accurate algebraic solutions in intermediate cycles of the classical AFEM with the application of a prolongation step, followed by a fixed number of few smoothing steps. The method reduces the overall computational cost of AFEM by providing a fast procedure for the construction of a quasi-optimal mesh sequence with large algebraic error in the intermediate cycles. Indeed, even though the intermediate solutions are far from the exact algebraic solutions, we show that their a-posteriori error estimation produces a refinement pattern that is substantially equivalent to the one that would be generated by classical AFEM, at a considerable fraction of the computational cost. In this talk, we will quantify rigorously how the error propagates throughout the algorithm, and then we will provide a connection with classical a posteriori error analysis. Finally, we will present a series of numerical experiments that highlights the efficiency and the computational speedup of S-AFEM.
submitted by S. Schmidt (sschmidt@math.hu-berlin.de, 2093 45330)