In this paper we propose and analyze stable variational formulations for convection diffusion
problems starting from concepts introduced by Sangalli. We derive efficient and reliable a …

We study theoretical and practical issues arising in the implementation of the Finite Element
Method for a strongly elliptic second order equation with jump discontinuities in its …

Since their emergence in the early 1950s, finite element methods have become one of the
most versatile and powerful methodologies for the approximate numerical solution of partial …

To deal with the divergence-free constraint in a double curl problem, \rmcurl\,μ^-1\rmcurl\,u=f
and \rmdiv\,εu=0 in Ω, where μ and ε represent the physical properties of the materials …

With the rise in popularity of compatible finite element, finite difference, and finite volume
discretizations for the time domain eddy current equations, there has been a corresponding …

An element-local L^2-projected C^0 finite element method is presented to approximate the
nonsmooth solution being not in H^1 of the Maxwell problem on a nonconvex Lipschitz …

We investigate new PDE discretization approaches for solving variational formulations with
different types of trial and test spaces. The general mixed formulation we consider assumes …

In this paper, we propose and analyze a mixed H^1-conforming finite element method for
solving Maxwell's equations in terms of electric field and Lagrange multiplier, where the …

A number of non-standard finite element methods have been proposed in recent years, each
of which derives from a specific class of PDE-constrained norm minimization problems. The …

In this paper, we propose and analyze a nodal-continuous and H 1-conforming finite
element method for the numerical computation of Maxwell's equations, with singular solution …