An Adaptive H-refinement Finite Element Method for Parabolic Differential Systems in Three Space Dimensions

I describe an adaptive h-reenement method for solving systems of parabolic partial diierential 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 reenement and coarsening. A more eecient algorithm for assembling banded portions of the Jacobian is introduced. A simple strategy for dealing with storage limitations by limiting the level of reenement is developed. Computational results demonstrate the eeectiveness of the adaptive method on linear and nonlinear problems.