Talk
Towards Finite Element Tensor Calculus
Talk by Dr. Kaibo Hu
Date: 10.04.24 Time: 16.30 - 18.00 Room: ETH HG E 1.2
Finite Element Exterior Calculus (FEEC) provides a cohomology framework for structure-preserving discretisation of a large class of PDEs. Differential complexes are important tools in FEEC. The de Rham complex is a basic example, with applications in curl-div related problems such as the Maxwell equations. There is a canonical finite element discretisation of the de Rham complex, which in the lowest order case coincides with discrete differential forms (Whitney forms). Different problems involve different complexes. In this talk, we provide an overview of some efforts towards Finite Element Tensor Calculus, inspired by tensor-valued problems from continuum mechanics and general relativity. On the continuous level, we systematically derive new complexes from the de Rham complexes. On the discrete level, We review the idea of distributional finite elements, and use them to obtain analogies of the Whitney forms for these new complexes. A special case is Christiansen’s finite element interpretation of Regge calculus, a discrete geometric scheme for metric and curvature.