An Adaptive H-Refinement Finite Element Method for Reaction-Diffusion Systems in Three Space Dimensions
I describe an adaptive h-refinement method for solving systems of parabolic differential equations in three space dimensions on hexahedral grids. These grids typically have irregular (hanging) nodes. Solutions are calculated using Galerkin's method with a piecewise trilinear basis in space and a BDF code in time. New a posteriori error indicators based on interpolation error estimates for irregular grids are used to control refinement and coarsening. A more efficient algorithm for assembling banded portions of the Jacobian is introduced. A simple strategy for dealing with storage limitations by limiting the level of refinement is developed. Computational results demonstrate the effectiveness of the adaptive method on linear and nonlinear problems.