Quenching for semidiscretizations of a semilinear heat equation with Dirichlet and Neumann boundary conditions

Diabate Nabongo; Théodore K. Boni

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

Numerical blow-up time for a semilinear parabolic equation with nonlinear boundary conditions.

Assalé, Louis A., Boni, Théodore K., Nabongo, Diabate (2008)

Journal of Applied Mathematics

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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 $L^{\infty}$ , respectively, of the scheme are established. Under certain hypotheses on the data, we also derive $L^{1}$ convergence without any convergence...

Asymptotic behavior for discretizations of a semilinear parabolic equation with a nonlinear boundary condition.

Diabate, Nabongo, Boni, Théodore K. (2008)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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Galerkin approximations for the linear parabolic equation with the third boundary condition

István Faragó, Sergey Korotov, Pekka Neittaanmäki (2003)

Applications of Mathematics

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We solve a linear parabolic equation in $ℝ^{d}$ , $d \geq 1,$ with the third nonhomogeneous boundary condition using the finite element method for discretization in space, and the $θ$ -method for discretization in time. The convergence of both, the semidiscrete approximations and the fully discretized ones, is analysed. The proofs are based on a generalization of the idea of the elliptic projection. The rate of convergence is derived also for variable time step-sizes.

A second-order finite volume element method on quadrilateral meshes for elliptic equations

Min Yang (2006)

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

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In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in $H^{1}$ -norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method.