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Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell’s equations

Ludovic Moya (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we study the temporal convergence of a locally implicit discontinuous Galerkin method for the time-domain Maxwell’s equations modeling electromagnetic waves propagation. Particularly, we wonder whether the method retains its second-order ordinary differential equation (ODE) convergence under stable simultaneous space-time grid refinement towards the true partial differential equation (PDE) solution. This is not a priori clear due to the component splitting which can introduce order...

Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell’s equations∗

Ludovic Moya (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The discrete compactness property for anisotropic edge elements on polyhedral domains

Ariel Luis Lombardi (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We prove the discrete compactness property of the edge elements of any order on a class of anisotropically refined meshes on polyhedral domains. The meshes, made up of tetrahedra, have been introduced in [Th. Apel and S. Nicaise, Math. Meth. Appl. Sci. 21 (1998) 519–549]. They are appropriately graded near singular corners and edges of the polyhedron.

The discrete compactness property for anisotropic edge elements on polyhedral domains∗

Ariel Luis Lombardi (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Two-sided symmetric condition in the analysis of magnetic fields with permanent magnets

František Melkes (2005)

Applications of Mathematics

Mathematical treatment of a planar magnetic field excited by permanent magnets is presented. A special two-sided condition for differential magnetic reluctivity is introduced to prove the unique existence of both the weak and the approximate solutions and also a certain error estimate. Notes to numerical algorithm and practical applications are given.