Sparse grid approximation spaces for space–time boundary integral formulations of the heat equation

Chernov, Alexey; Reinarz, Anne

Abstract

The aim of this paper is to develop and analyse stable and accurate numerical approximation schemes for boundary integral formulations of the heat equation with Dirichlet boundary conditions. The accuracy of Galerkin discretisations for the resulting boundary integral formulations strongly depends on the choice of discretisation space. We develop a-priori error analysis utilising a proof technique that involves norm bounds in hierarchical wavelet subspace decompositions. We apply this to full tensor product discretisations and anisotropic sparse grid discretisations and demonstrate improvements over existing results in both cases. Finally, a simple adaptive scheme is proposed to suggest an optimal shape for the sparse grid index sets.

• Journal Article Type: Article
• Acceptance Date: Jun 8, 2019
• Online Publication Date: Oct 24, 2019
• Publication Date: Dec 1, 2019
• Deposit Date: Aug 20, 2020
• Journal: Computers and Mathematics with Applications
• Print ISSN: 0898-1221
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 78
• Issue: 11
• Pages: 3605-3619
• DOI: https://doi.org/10.1016/j.camwa.2019.06.036
• Public URL: https://durham-repository.worktribe.com/output/1294245
• Related Public URLs: https://arxiv.org/abs/1804.10986