EXTRAPOLATION AND A-POSTERIORI ERROR ESTIMATORS OF PETROV-GALERKIN METHODS FOR NON-LINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

• 来源期刊: 计算数学（英文版）
• 学科: 数学
• 关键词: Volterra integro-differential equations Petrov-Galerkin finite element methods Asymptotic expansions Interpolation post-processing A-posteriori error estimators.
• 年，卷（期）: 2001,（4）
• 页码范围: 407-422
• 页数: 16页
• 分类号: O1
• 语种: 英文

摘要

In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initialvalue problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of aposteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.