Convergence and Optimality of an Adaptive Mixed Finite Element
Method on Surfaces
Adam Mihalik
UCSD
Abstract:
Finite element exterior calculus (FEEC) is a framework that allows for
results proved on general differential complexes to be applied to a
large class of mixed finite element problems. In earlier work, using
this framework, we introduced a convergence and optimality result for a
class of adaptive mixed finite element problems posed on polygonal
domains. In this talk we discuss the extension of these results to
problems on Euclidean hypersurfaces. More specifically, we introduce a
method and prove rates of convergence for problems posed on surfaces
implicitly represented by level-sets of smooth functions.