Numerical Solution of a parabolic system with blowup of the solution

In this paper, the author proposes a numerical method to solve a parabolic system of two quasilinear equations of nonlinear heat conduction with sources. The solution of this system may blow up in finite time. It is proved that the numerical solution also may blow up in finite time and an estimate of this time is obtained. The convergence of the scheme is obtained for particular values of the parameters.Comment: 22 page

Analysis of completely discrete finite element method for a free boundary diffusion problem with absorption

AbstractConvergence of truncation methods is obtained for a free boundary problem in R2 with an absorption depending on space and time. Error estimates are derived for the discretization, in space by a P1-finite element method and in time by a backward Euler method

Numerical Solution of a nonlinear reaction-diffusion problem in the case of HS-regime

In this paper, the authors propose a numerical method to compute the solution of a nonlinear reaction-diffusion problem in the case of HS-regime. The initial condition is a nonnegative function with compact support. The problem is split in two parts: A hyperbolic term solved by using the Hopf and Lax formula and a parabolic term solved by a backward linearized Euler method in time and a finite element method in space. Estimates of the numerical solution are obtained and it is proved that any numerical solution blows up in finite time