Finite volume approximation of stiff problems on two-dimensional curvilinear domain. Issue 10 (2nd October 2016)

• Record Type: Journal Article
• Authors: Faure, Sylvain; Tekitek, Mohamed Mahdi; Temam, Roger
• Is Part Of: International journal of computer mathematics. Volume 93:Issue 10(2016)
• Page Start: 1787
• Page End: 1799
• Publication Date: 2016-10-02
• Subjects: finite volume methods -- boundary layers -- correctors -- stiff problems; 65N08 -- 76F40 -- 65L04; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2015.1075013
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : The aim of this article is to apply a novel finite volume method to approximate a stiff problem for a two-dimensional curvilinear domain. The stiffness is caused by the existence of a small parameter in the equation which introduces a boundary layer along parts of the curvilinear boundary. Incorporating in the finite volume space the boundary layer correctors, the boundary layer singularities are absorbed. Hence, we propose a second order scheme for curvilinear domains using uniform meshes thus avoiding the costly refinement of mesh in the boundary layers.