LUMPED-MASS FINITE-ELEMENT METHOD WITH INTERPOLATION OF THE NONLINEAR COEFFICIENTS FOR A QUASILINEAR HEAT TRANSFER EQUATION

摘要

A unified numerical technique for computing single-point, regional, and total blow-up solutions of quasilinear heat transfer equations in the radial symmetric care is proposed and realized. It is based on the lumped-mass-finite-element method in space, with interpolation of the nonlinear coefficients and explicit methods for solving the system of ordinary differential equations. A special mesh adaptation, consistent with the structure of the known self-similar solution, is realized for the cases of single point and total blow-up. This gives a possibility to calculate the solution close to the blow-up time and so to analyze its asymptotic behavior. [References: 25]