DK4: Nonstandard Finite Element Solvers for Second-Order Elliptic Boundary Value Problems

We propose to investigate non-standard finite element schemes for solving second-order elliptic boundary value problems. The construction of these finite element schemes are based on boundary element technologies and interface-concentrated finite element techniques. The first approach allows us to treat polyhedral and even more general meshes, whereas the second technique can easily handle subdomains
with complicated interfaces and/or complicated behavior of solution along these interfaces. The combination of both discretization techniques and their coupling with data-sparse boundary element discretizations are feasible. The construction of fast and highly efficient parallel solvers for the corresponding systems of algebraic equations is the ultimative goal of this project.

Supervisor: Prof. Ulrich Langer