Penalty-combined approaches to the Ritz-Galerkin and finite element methods for singularity problems of elliptic equations

✍ Scribed by Zi-Cai Li

• Publisher: John Wiley and Sons
• Year: 1992
• Tongue: English
• Weight: 885 KB
• Volume: 8
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.1690080103

✦ Synopsis

Penalty coupling techniques on an interface boundary, artificial or material, are first presented for combining the Ritz-Galerkin and finite element methods. An optimal convergence rate first is proved in the Soboiev norms. Moreover, a significant coupling strategy, L + 1 = O((1n h(), between these two methods are derived for the Laplace equation with singularities, where t + 1 is the total number of particular solutions used in the Ritz-Galerkin method, and h is the maximal boundary length of quasiuniform elements used in the linear finite element method. Numerical experiments have been carried out for solving the benchmark model: Motz's problem. Both theoretical analysis and numerical experiments clearly display the importance of penalty-combined methods in solving elliptic equations with singularities.