Handling corner singularities by the mortar spectral element method

Abstract

The solution of an elliptic partial differential equation in a polygon can be written as a linear combination of singular functions, which only depend on the geometry of the domain, and of a more regular part. The aim of this paper is double: presenting an efficient algorithm to approximate the solution despite the singularities, computing a high accuracy approximation of the coefficient of the leading singularity. Both results rely on the mortar spectral element method.

Keywords:

• Spectral element method
• mortar method
• corner domains
• singularities

AMS:

• 65N30
• 35A35
• 65N15