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Displaying 461 –
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760
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...
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 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 and absolute stability is deffined in terms of the real parameters and . Sufficient conditions are illustrated for - methods and for combinations of Adams-Moulton and backward differentiation methods.
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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