Analysis of a space–time continuous Galerkin method for convection-dominated Sobolev equations. (15th April 2017)

• Record Type: Journal Article
• Authors: Zhao, Zhihui; Li, Hong; Luo, Zhendong
• Is Part Of: Computers & mathematics with applications. Volume 73:issue 8(2017)
• Page Start: 1643
• Page End: 1656
• Publication Date: 2017-04-15
• Subjects: Continuous Galerkin method -- Sobolev equations with convection-dominated terms -- Optimal convergence rates -- Numerical examples; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.01.023
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: The convergence of space–time continuous Galerkin (STCG) method for the Sobolev equations with convection-dominated terms is studied in this article. It allows variable time steps and the change of the spatial mesh from one time interval to the next, which can make this method suitable for numerical simulations on unstructured grids. We prove the existence and uniqueness of the approximate solution and get the optimal convergence rates in L ∞ ( H 1 ) norm which do not require any restriction assumptions on the space and time mesh size. Finally, some numerical examples are designed to validate the high efficiency of the method showed herein and to confirm the correctness of the theoretical analysis.