2018/04/29 by Alexey Chernov, Chernov, Alexey, Anne Reinarz +1
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1804.10986
openalex publication_date 2018/04/29 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
The aim of this paper is to develop stable and accurate numerical schemes for\nboundary integral formulations of the heat equation with Dirichlet boundary\nconditions. The accuracy of Galerkin discretisations for the resulting boundary\nintegral formulations depends mainly on the choice of discretisation space. We\ndevelop a-priori error analysis utilising a proof technique that involves norm\nequivalences in hierarchical wavelet subspace decompositions. We apply this to\na full tensor product discretisation, showing improvements over existing\nresults, particularly for discretisation spaces having low polynomial degrees.\nWe then use the norm equivalences to show that an anisotropic sparse grid\ndiscretisation yields even higher convergence rates. Finally, a simple adaptive\nscheme is proposed to suggest an optimal shape for the sparse grid index sets.\n