Displaying similar documents to “Asymptotic behavior for discretizations of a semilinear parabolic equation with a nonlinear boundary condition.”

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

Diabate Nabongo, Théodore K. Boni (2008)

Commentationes Mathematicae Universitatis Carolinae

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This paper concerns the study of the numerical approximation for the following boundary value problem: u t ( x , t ) - u x x ( x , t ) = - u - p ( x , t ) , 0 < x < 1 , t > 0 , u x ( 0 , t ) = 0 , u ( 1 , t ) = 1 , t > 0 , u ( x , 0 ) = u 0 ( x ) > 0 , 0 ≤ x ≤ 1 , where p > 0 . We obtain some conditions under which the solution of a semidiscrete form of the above problem quenches in a finite time and estimate its semidiscrete quenching time. We also establish the convergence of the semidiscrete quenching time. Finally, we give some numerical experiments to illustrate our analysis.

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...