Finite and spectral element methods on unstructured grids for flow and wave propagation problems

Abstract

Finite element methods are one of the most prominent discretisation techniques for the solution of partial differential equations. They provide high geometric flexibility, accuracy and robustness, and a rich body of theory exists. In this chapter, we summarise the main principles of Galerkin finite element methods, and identify and discuss avenues for their parallelisation. We develop guidelines that lead to efficient implementations, however, we prefer generic ideas and principles over utmost performance tuning.