Finite volume approximation of stiff problems on two-dimensional curvilinear domain

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.

Keywords:

• finite volume methods
• boundary layers
• correctors
• stiff problems

2010 AMS Subject Classifications:

• 65N08
• 76F40
• 65L04

Disclosure

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the NSF Grants DMS 1206438, and by the Research Fund of Indiana University.