Martin Licht: Thursday, 06th February 2025 at 10:00
Abstract: Structure-preserving numerical methods have had a transformative impact on the numerical analysis of partial differential equations, reproducing the fundamental mathematical structures of numerous partial differential equations exactly at the numerical level. This talk gives an introduction and overview of structure-preserving finite element methods via “finite element exterior calculus” (FEEC) and explores some new directions in the field. FEEC is a comprehensive framework for mixed finite element methods, at the heart of which are finite element differential complexes. This comprehensive theory of mixed finite element methods connects geometry, topology, and classical numerical analysis. We highlight recent research developments, including mixed boundary conditions in FEEC and finite element methods over manifolds, and discuss some future directions in numerical electromagnetism, elasticity, and fluid dynamics.
