数值积分对完全非线性抛物型积分微分方程有限元方法的影响

摘要

We study the effect of numerical integration in Finite Element methods for more general nonlinear parabolic integrodifferential equations. We then extend the results of to include problems where the term u t is replaced by the term c(x,u) t , and give some sufficient conditions to ensure that the order of convergence is unaltered in the presence of numerical integration. Optimal L 2 and H 1 error estimates are established.