Parallel space-time hp adaptive discretization scheme for parabolic problems

We introduce an integration scheme for parabolic problems. Our parallelizable method uses adaptive hp-finite elements in space, and finite differences in time. The strategy can also be combined with a classical finite element method parallelization technique based on domain decomposition. We verified the performance of our method against two different benchmarks, in both two-dimensional (model problem on an L-shaped domain) and three-dimensional (Pennes bioheat equation) settings. Results show a significant speedup in computational time when compared with the sequential version of the algorithm. Moreover, we develop a mathematical framework to analyze similar schemes which include hp spatial adaptivity. Our framework describes error propagation rigorously, and as such allows to analyze convergence properties of these mixed methods. (C) 2017 Elsevier B.V. All rights reserved.