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

Assalé, Louis A.; Boni, Théodore K.; Nabongo, Diabate

Displaying similar documents to “Numerical blow-up time for a semilinear parabolic equation with nonlinear boundary conditions.”

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: $\{\begin{matrix} u_{t} (x, t) - u_{x x} (x, t) = - u^{- p} (x, t), & 0 < x < 1, t > 0, u_{x} (0, t) = 0, & u (1, t) = 1, t > 0, u (x, 0) = u_{0} (x) > 0, & 0 \leq x \leq 1, \end{matrix}$ 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.

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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Continuity of the quenching time for a parabolic equation with a nonlinear boundary condition and a potential.

Boni, Théodore K., N'gohisse, Firmin K. (2009)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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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...

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.