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Displaying 461 – 480 of 760

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Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements

Salvatore Caorsi, Paolo Fernandes, Mirco Raffetto (2001)

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

By using an inductive procedure we prove that the Galerkin finite element approximations of electromagnetic eigenproblems modelling cavity resonators by elements of any fixed order of either Nedelec’s edge element family on tetrahedral meshes are convergent and free of spurious solutions. This result is not new but is proved under weaker hypotheses, which are fulfilled in most of engineering applications. The method of the proof is new, instead, and shows how families of spurious-free elements can...

Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements

Salvatore Caorsi, Paolo Fernandes, Mirco Raffetto (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

By using an inductive procedure we prove that the Galerkin finite element approximations of electromagnetic eigenproblems modelling cavity resonators by elements of any fixed order of either Nedelec's edge element family on tetrahedral meshes are convergent and free of spurious solutions. This result is not new but is proved under weaker hypotheses, which are fulfilled in most of engineering applications. The method of the proof is new, instead, and shows how families of spurious-free elements...

Stability analysis of reducible quadrature methods for Volterra integro-differential equations

Vernon L. Bakke, Zdzisław Jackiewicz (1987)

Aplikace matematiky

Stability analysis for numerical solutions of Voltera integro-differential equations based on linear multistep methods combined with reducible quadrature rules is presented. The results given are based on the test equation y ' ( t ) = γ y ( t ) + 0 t ( λ + μ t + v s ) y ( s ) d s and absolute stability is deffined in terms of the real parameters γ , λ , μ and v . Sufficient conditions are illustrated for ( 0 ; 0 ) - methods and for combinations of Adams-Moulton and backward differentiation methods.

Stability analysis of the Interior Penalty Discontinuous Galerkin method for the wave equation

Cyril Agut, Julien Diaz (2013)

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

We consider here the Interior Penalty Discontinuous Galerkin (IPDG) discretization of the wave equation. We show how to derive the optimal penalization parameter involved in this method in the case of regular meshes. Moreover, we provide necessary stability conditions of the global scheme when IPDG is coupled with the classical Leap–Frog scheme for the time discretization. Numerical experiments illustrate the fact that these conditions are also sufficient.

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