Efficient solvers for hp-adaptive finite element methods
hp-adaptive finite element methods allow to choose both the mesh size h and the polynomial degree p locally on every cell. Despite their excellent convergence properties, these methods are not widely used, likely due to the complexities involved in their implementation. To facilitate their use, we have recently introduced comprehensive support for hp-adaptive methods in the open-source library deal.II, including parallel computation capabilities for continuous Galerkin methods.
In this presentation, we will explore the general idea behind hp-adaptive finite element methods, address challenges encountered in their parallel implementation, and showcase example applications developed using the deal.II library. Particular attention will be given to the design of efficient solvers for the resulting systems of equations.
