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Sparse space‐time Galerkin BEM for the nonstationary heat equation
Author(s) -
Chernov A.,
Schwab Ch.
Publication year - 2013
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201100192
Subject(s) - mathematics , galerkin method , tensor product , discontinuous galerkin method , mathematical analysis , tensor (intrinsic definition) , boundary (topology) , boundary value problem , rate of convergence , finite element method , computer science , geometry , pure mathematics , physics , computer network , channel (broadcasting) , thermodynamics
We 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.