Experiments with an Adaptive h-, p-, and r-Refinement Finite Element Method forParabolic Systems

摘要

We describe an adaptive finite element method of lines for solving initial-boundary value problems for vector systems of parabolic partial differential equations in one and two space dimensions. The method contains capabilities for using h-, p-, and r-refinement strategies either singly or in combination. Results of several one-dimensional examples point to the superiority of hp-refinement relative to h-, p-, hr-, or pr-refinement. Preliminary results are