A Nodal-based Finite Element Approximation of the Maxwell Problem Suitable for Singular Solutions

Authors:
Santiago Badia;Ramon Codina
Affiliations:
sbadia@cimne.upc.edu;ramon.codina@upc.edu
Venue:
SIAM Journal on Numerical Analysis
Year:
2012

Citing 12
Cited 1

Mixed and hybrid finite element methods

Mixed and hybrid finite element methods
The origin of spurious solutions in computational electromagnetics

Journal of Computational Physics
On the solution of time-harmonic scattering problems for Maxwell's equations

SIAM Journal on Mathematical Analysis
Edge Elements on Anisotropic Meshes and Approximation of the Maxwell Equations

SIAM Journal on Numerical Analysis
Numerical solution to the time-dependent Maxwell equations in axisymmetric singular domains: the singular complement method

Journal of Computational Physics
Mixed Discontinuous Galerkin Approximation of the Maxwell Operator

SIAM Journal on Numerical Analysis
Mixed finite element methods for stationary incompressible magneto–hydrodynamics

Numerische Mathematik
Interior penalty discontinuous Galerkin method for Maxwell's equations: Energy norm error estimates

Journal of Computational and Applied Mathematics
Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales

Applied Numerical Mathematics
The Local $L^2$ Projected $C^0$ Finite Element Method for Maxwell Problem

SIAM Journal on Numerical Analysis
Unified Stabilized Finite Element Formulations for the Stokes and the Darcy Problems

SIAM Journal on Numerical Analysis
Solving electromagnetic eigenvalue problems in polyhedral domains with nodal finite elements

Numerische Mathematik

On an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics

Journal of Computational Physics

Quantified Score

Hi-index	0.01

Visualization

Abstract

A new mixed finite element approximation of Maxwell's problem is proposed, its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh dependent stabilizing term, which yields a very weak control on the divergence of the unknown. The method is shown to be stable and convergent in the natural $H({\rm \mathbf{curl}}\, 0; \Omega)$ norm for this unknown. In particular, convergence also applies to singular solutions, for which classical nodal-based interpolations are known to suffer from spurious convergence upon mesh refinement.