1er Symposium canadien en analyse numérique et calcul scientifique
A Simple Moving Mesh Method for Blow-up Problems
Chen, George
Cape Breton University

We develop a simple and efficient adaptive mesh generator for time-dependent partial differential equations with singular solutions in two dimensional spaces. The mesh generator is based on minimizing the sum of two diagonal lengths in each cell. we also add second order difference terms to obtain smoother and more orthogonal mesh. The method is successfully applied to the nonlinear heat equations with blow-up solutions. We can obtain a solution with an amplitude of $10^{15}$ at the peak and the mesh difference of $10^{-15}$ near the peak. We also discuss nonlinear heat equations whose solutions blow up at space infinity and the blow-up time is given.

Mardi, 18 juin, 10h30
Salle Des Plaines B