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Displaying similar documents to “Gaussian quadrature rules and A -stability of Galerkin schemes for ODE.”

Stability of ALE discontinuous Galerkin method with Radau quadrature

Vlasák, Miloslav

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We assume the nonlinear parabolic problem in a time dependent domain, where the evolution of the domain is described by a regular given mapping. The problem is discretized by the discontinuous Galerkin (DG) method modified by the right Radau quadrature in time with the aid of Arbitrary Lagrangian-Eulerian(ALE) formulation. The sketch of the proof of the stability of the method is shown.

Arbitrary high-order finite element schemes and high-order mass lumping

Sébastien Jund, Stéphanie Salmon (2007)

International Journal of Applied Mathematics and Computer Science

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Computers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with high-order methods. In this article we will consider Lagrange finite elementsof order k and show how it is possible to automatically generate the mass and stiffness matrices of any order with the help of symbolic computation software. We compare two high-order time discretizations: an explicit one using a Taylor expansion in time (a Cauchy-Kowalewski procedure) and an implicit...