@misc{OevermannKlein2006, author = {Oevermann, Michael and Klein, Rupert}, title = {A cartesian grid finite volume method for the solution of the Poisson equation with variable coefficients and embedded interfaces}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8996}, number = {06-05}, year = {2006}, abstract = {We present a finite volume method for the solution of the two-dimensional Poisson equation \$ \nabla\cdot( \beta( {\mbox{\boldmath \$x\$}}) \nabla u({\mbox{\boldmath \$x\$}})) = f(\mbox{\boldmath \$x\$}) \$ with variable, discontinuous coefficients and solution discontinuities on irregular domains. The method uses bilinear ansatz functions on Cartesian grids for the solution \$u({\mbox{\boldmath \$x\$})\$ resulting in a compact nine-point stencil. The resulting linear problem has been solved with a standard multigrid solver. Singularities associated with vanishing partial volumes of intersected grid cells or the dual bilinear ansatz itself are removed by a two-step asymptotic approach. The method achieves second order of accuracy in the \$L^\infty\$ and \$L^2\$ norm.}, language = {en} }