Post-processing discontinuous Galerkin solutions to Volterra integro-differential equations: Analysis and simulations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:253

Article

Mustapha, Kassem¹  Ryan, Jennifer K.^2,3 

[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

[2] Univ E Anglia, Sch Math, Norwich NR4 7TJ, Norfolk, England

[3] Delft Univ Technol, Delft Inst Appl Math, NL-2600 AA Delft, Netherlands

关键词: Integro-differential equation;    Singular kernel;    Smooth kernel;    Discontinuous Galerkin;    Superconvergence;    Post-processing;   

DOI  :  10.1016/j.cam.2013.03.047

来源: Elsevier

【 摘 要 】

This paper presents a superconvergence extraction technique for Volterra integro-differential equations with smooth and non-smooth kernels. Specifically, extracting superconvergence is done via a post-processed discontinuous Galerkin (DG) method obtained from interpolating the DG solution using Lagrange polynomials at the nodal points. A global superconvergence error bound (in the L-infinity-norm) is established. For a non-smooth kernel, a family of non-uniform time meshes is used to compensate for the singular behaviour of the exact solution near t = 0. The derived theoretical results are numerically validated in a sample of test problems, demonstrating higher-than-expected convergence rates. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free