Talk:Extended finite element method: Difference between revisions

Revision as of 22:54, 6 July 2013

Revision as of 00:50, 8 July 2013

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The article doesn't explain in much detail how this method differs from standard finite elements. Is it just standard finite elements with a certain class of discontinuous or non-smooth basis functions, or is there more to it than that? —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 22:54, 6 July 2013 (UTC)

:Someone can correct me if this is wrong, but my understanding is that the "standard finite elements" involve constructing spaces that span polynomial spaces so that the Bramble-Hilbert lemma can be applied to guarantee convergence. Extended finite elements involve adding more basis functions not designed to span polynomial spaces (needed for approximation estimates) but for building equation specific information into the solution. If you look at the abstract of the Babuska-Melenk paper, they describe the PUM method as "a new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved". The X-FEM literature is a little more complex, involving building geometric features that don't have to be meshed into the solution (as another contributer mentions above). [[User:RuppertsAlgorithm|RuppertsAlgorithm]] ([[User talk:RuppertsAlgorithm|talk]]) 00:50, 8 July 2013 (UTC)