Galerkin finite element method for a class of porous medium equations Export

@article{citeulike:3479323, abstract = {We study the numerical approximation of the Saturation Equation which arises in the formulation of two phase fluid flow through porous media, idealized as either a convex bounded polyhedral domain or a domain with smooth boundary. This equation is degenerate and the solutions are not guaranteed to be sufficiently smooth for direct numerical approximation. Through regularization, a family of approximate non-degenerate problems is considered along with their numerical approximations. Error estimates are established for appropriately transformed continuous Galerkin approximations, followed by corresponding error estimates for a fully discretized Galerkin method for this class of problems.}, author = {Fadimba, K.}, citeulike-article-id = {3479323}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.nonrwa.2003.07.001}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S1468-1218(03)00054-3}, doi = {10.1016/j.nonrwa.2003.07.001}, issn = {14681218}, journal = {Nonlinear Analysis: Real World Applications}, keywords = {equation, fem, medium, non-linear, pde, porous}, month = {April}, number = {2}, pages = {355--387}, posted-at = {2008-11-04 16:43:53}, priority = {2}, title = {Galerkin finite element method for a class of porous medium equations}, url = {http://dx.doi.org/10.1016/j.nonrwa.2003.07.001}, volume = {5}, year = {2004} }

TY - JOUR ID - citeulike:3479323 L3 - citeulike-article-id:3479323 N2 - We study the numerical approximation of the Saturation Equation which arises in the formulation of two phase fluid flow through porous media, idealized as either a convex bounded polyhedral domain or a domain with smooth boundary. This equation is degenerate and the solutions are not guaranteed to be sufficiently smooth for direct numerical approximation. Through regularization, a family of approximate non-degenerate problems is considered along with their numerical approximations. Error estimates are established for appropriately transformed continuous Galerkin approximations, followed by corresponding error estimates for a fully discretized Galerkin method for this class of problems. IS - 2 JF - Nonlinear Analysis: Real World Applications SN - 14681218 EP - 387 TI - Galerkin finite element method for a class of porous medium equations VL - 5 SP - 355 KW - equation KW - fem KW - medium KW - non-linear KW - pde KW - porous AU - Fadimba, K PY - 2004/04// UR - http://dx.doi.org/10.1016/j.nonrwa.2003.07.001 ER -