Comparison of the Finite Difference and Finite Element Methods for the Solution of the Transient Heat Conduction Equation with Temperature-Dependent Conductivity.

摘要

The transient heat conduction equation with a nonlinear conductivity is solved using three finite difference schemes and two finite element schemes. The schemes are compared for speed and accuracy against an analytic solution. The finite element methods are shown to be the most accurate and one, a lumped mass method, is comparable in speed to the finite difference methods. The lumped mass finite element method is shown to be the clear choice from among the methods tested in solving the test problem. (Author)