A study of moving mesh PDE methods for numerical simulation of blowup in reaction diffusion equations

Abstract

A new concept called the dominance of equidistribution is introduced for analyzing moving mesh partial differential equations for numerical simulation of blowup in reaction diffusion equations. Theoretical and numerical results show that a moving mesh method works successfully when the employed moving mesh equation has the dominance of equidistribution. The property can be verified using dimensional analysis. In several aspects the current work generalizes previous work where a moving mesh equation is shown to have this dominance of equidistribution if it preserves the scaling invariance of the underlying physical partial differential equation and uses a small, constant value for τ (a parameter used for adjusting response time of the mesh movement to the change in the physical solution). Also, cases with both constant and variable τ are considered here.