Displaying similar documents to “Quenching for semidiscretizations of a semilinear heat equation with Dirichlet and Neumann boundary conditions”

Combined finite element -- finite volume method (convergence analysis)

Mária Lukáčová-Medviďová (1997)

Commentationes Mathematicae Universitatis Carolinae

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We present an efficient numerical method for solving viscous compressible fluid flows. The basic idea is to combine finite volume and finite element methods in an appropriate way. Thus nonlinear convective terms are discretized by the finite volume method over a finite volume mesh dual to a triangular grid. Diffusion terms are discretized by the conforming piecewise linear finite element method. In the paper we study theoretical properties of this scheme for the scalar nonlinear convection-diffusion...

Finite element approximation for degenerate parabolic equations. An application of nonlinear semigroup theory

Akira Mizutani, Norikazu Saito, Takashi Suzuki (2005)

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

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Finite element approximation for degenerate parabolic equations is considered. We propose a semidiscrete scheme provided with order-preserving and L 1 contraction properties, making use of piecewise linear trial functions and the lumping mass technique. Those properties allow us to apply nonlinear semigroup theory, and the wellposedness and stability in L 1 and L ∞ , respectively, of the scheme are established. Under certain hypotheses on the data, we also derive L 1 convergence without any convergence...