Premium
A projection penalization approach for the high‐order DG‐FEM in the time domain
Author(s) -
Gjonaj E.,
Weiland T.
Publication year - 2011
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/2011rs004671
Subject(s) - spurious relationship , charge conservation , finite element method , curl (programming language) , discontinuous galerkin method , conservation law , projector , mathematics , projection (relational algebra) , galerkin method , mathematical analysis , maxwell's equations , wave equation , domain (mathematical analysis) , conservation of energy , physics , charge (physics) , computer science , algorithm , quantum mechanics , statistics , optics , thermodynamics , programming language
We investigate the Discontinuous Galerkin‐Finite Element Method (DG‐FEM) for the solution of Maxwell's equations in the time domain. The charge conservation laws are known to be violated by this method which consequently gives rise to spurious numerical solutions. It is, however, possible to introduce additional constrains in the formulation which impose charge conservation either exactly or approximately. In this work, a new approach based on a topological orthogonal projector into a high‐order H ( curl )‐conforming approximation space is proposed. Using this approach we derive a constrained DG‐FEM formulation which is strictly free of spurious modes. Furthermore, we construct a time domain penalization scheme which allows to separate the spurious modes related to unphysical charges from the physical solutions while maintaining accuracy and energy conservation.