We develop the analysis of stabilized sparse tensor-product finite element methods for high-dimensional, non-self-adjoint and possibly degenerate second-order partial differential equations of the form , , where is a symmetric positive semidefinite matrix, using piecewise polynomials of degree . Our convergence analysis is based on new high-dimensional approximation results in sparse tensor-product spaces. We show that the error between the analytical solution and its stabilized sparse finite element approximation on a partition of of mesh size satisfies the following bound in the streamline-diffusion norm , provided belongs to the space of functions with square-integrable mixed st derivatives:
Mots clés : high-dimensional Fokker-Planck equations, partial differential equations with nonnegative characteristic form, sparse finite element method
@article{M2AN_2008__42_5_777_0, author = {Schwab, Christoph and S\"uli, Endre and Todor, Radu Alexandru}, title = {Sparse finite element approximation of high-dimensional transport-dominated diffusion problems}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {777--819}, publisher = {EDP-Sciences}, volume = {42}, number = {5}, year = {2008}, doi = {10.1051/m2an:2008027}, mrnumber = {2454623}, zbl = {1159.65094}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2008027/} }
TY - JOUR AU - Schwab, Christoph AU - Süli, Endre AU - Todor, Radu Alexandru TI - Sparse finite element approximation of high-dimensional transport-dominated diffusion problems JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2008 SP - 777 EP - 819 VL - 42 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2008027/ DO - 10.1051/m2an:2008027 LA - en ID - M2AN_2008__42_5_777_0 ER -
%0 Journal Article %A Schwab, Christoph %A Süli, Endre %A Todor, Radu Alexandru %T Sparse finite element approximation of high-dimensional transport-dominated diffusion problems %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 777-819 %V 42 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2008027/ %R 10.1051/m2an:2008027 %G en %F M2AN_2008__42_5_777_0
Schwab, Christoph; Süli, Endre; Todor, Radu Alexandru. Sparse finite element approximation of high-dimensional transport-dominated diffusion problems. ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 5, pp. 777-819. doi : 10.1051/m2an:2008027. http://www.numdam.org/articles/10.1051/m2an:2008027/
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