Chapter 5: Approximation of Hilbert complexes
Douglas N. Arnold · Society for Industrial and Applied Mathematics eBooks · 2018
Our goal now is to design and analyze numerical methods for the approximate solution of a Hodge Laplacian problem associated to some closed Hilbert complex. We shall use Galerkin methods, i.e., we shall replace the trial and test spaces occuring in the primal or mixed weak formulation by finite dimensional subspaces. In practice, when the Hilbert complex is the de Rham complex or something similar, the subspaces we consider will be finite element spaces.