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Advanced Numerical Methods in the Mathematical Sciences

Steffen Weißer, Saarland University (Germany)
Polygonal/Polyhedral discretizations with BEM-based Finite Element Methods


In the development of numerical methods to solve boundary value problems the requirement of flexible mesh handling gains more and more importance. The BEM-based finite element method is one of the new promising strategies which yields conforming approximations on polygonal and polyhedral meshes, respectively. This flexibility is obtained by special trial functions which are defined implicitly as solutions of local boundary value problems related to the underlying differential equation. Due to this construction, the approximation space already inherit some properties of the unknown solution. These implicitly defined trial functions are treated by means of boundary element methods (BEM) in the realization.