Solving the singular two-dimensional fourth order problem by the mortar spectral element method

• Main Authors: Mohamed Abdelwahed, Azhar Al Salam, Nejmeddine Chorfi
• Format: Article
• Language: English
• Published: SpringerOpen 2018-03-01
• Series: Boundary Value Problems
• Subjects: Biharmonic equation; Fourth order problem; Singularity; Strang and Fix algorithm; Mortar spectral element method
• Online Access: http://link.springer.com/article/10.1186/s13661-018-0960-8

Abstract In this work, we implement the mortar spectral element method for the biharmonic problem with a homogeneous boundary condition. We consider a polygonal domain with corners which relies on the mortar decomposition domain technique. We propose the Strang and Fix algorithm, which permits to enlarge the discrete space of the solution by the first singular function. The interest of this algorithm is the approximation of the solution and the leading singular coefficient which has a physical significance in the propagation of cracks. We give some numerical results which confirm the optimality of the order of the error.