Displaying similar documents to “Numerical solution of nonlinear diffusion with finite extinction phenomenon.”

An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems

Molati, Motlatsi, Murakawa, Hideki

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This paper deals with nonlinear diffusion problems which include the Stefan problem, the porous medium equation and cross-diffusion systems. We provide a linear scheme for these nonlinear diffusion problems. The proposed numerical scheme has many advantages. Namely, the implementation is very easy and the ensuing linear algebraic systems are symmetric, which show low computational cost. Moreover, this scheme has the accuracy comparable to that of the wellstudied nonlinear schemes and...

Contaminant transport with adsorption in dual-well flow

Jozef Kačur, Roger Van Keer (2003)

Applications of Mathematics

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Numerical approximation schemes are discussed for the solution of contaminant transport with adsorption in dual-well flow. The method is based on time stepping and operator splitting for the transport with adsorption and diffusion. The nonlinear transport is solved by Godunov’s method. The nonlinear diffusion is solved by a finite volume method and by Newton’s type of linearization. The efficiency of the method is discussed.

On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow

Vít Dolejší, Miloslav Feistauer, Christoph Schwab (2002)

Mathematica Bohemica

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The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume—finite element method. Its advantage is the use of only one mesh (in contrast to the combined...

Behaviour of the support of the solution appearing in some nonlinear diffusion equation with absorption

Tomoeda, Kenji

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Numerical experiments suggest interesting properties in the several fields of fluid dynamics, plasma physics and population dynamics. Among such properties, we may observe the interesting phenomena; that is, the repeated appearance and disappearance phenomena of the region penetrated by the fluid in the flow through a porous media with absorption. The model equation in two dimensional space is written in the form of the initial-boundary value problem for a nonlinear diffusion equation...