Sparse space‐time Galerkin BEM for the nonstationary heat equation

Abstract

AbstractWe construct and analyze sparse tensorized space‐time Galerkin discretizations for boundary integral equations resulting from the boundary reduction of nonstationary diffusion equations with either Dirichlet or Neumann boundary conditions. The approach is based on biorthogonal multilevel subspace decompositions and a weighted sparse tensor product construction. We compare the convergence behavior of the proposed method to the standard full tensor product discretizations. In particular, we show for the problem of nonstationary heat conduction in a bounded two‐ or three‐dimensional spatial domain that low order sparse space‐time Galerkin schemes are competitive with high order full tensor product discretizations in terms of the asymptotic convergence rate of the Galerkin error in the energy norms, under lower regularity requirements on the solution.