The implementation of high-order (spectral) approximations associated with FEM is an approach to overcome the difficulties encountered in the numerical analysis of complex problems. This paper proposes the use of the spectral finite element method, originally developed for computational fluid dynamics problems, to achieve improved solutions for these types of problems. Here, the interpolation n...

We discuss the application of the spectral element method to the monodomain and bidomain equations describing propagation of cardiac action potential. Models of cardiac electrophysiology consist of a system of partial differential equations coupled with a system of ordinary differential equations representing cell membrane dynamics. The solution of these equations requires solving multiple leng...

A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares; a finite element approximation is used on the first square and a spectral discretization is used on the second. Two kinds of matching conditions on the interface are presented and compared; in both cases, error estimates are proved.

We examine the dual graph representation of simplicial manifolds in causal dynamical triangulations (CDT) as a means to build observables and propose new based on finite element methods (FEM). In particular, with application FEM techniques, we extract (low-lying) spectrum Laplace-Beltrami (LB) operator Sobolev space ${H}^{1}$ scalar functions piecewise flat compare them corresponding results ob...