Uniform convergence and preconditioning methods for projection nonconforming and mixed methods for nonselfadjoint and indefinite problems

✍ Scribed by Jinru Chen; Likang Li

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 172 KB
• Volume: 185
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(99)00347-3

✦ Synopsis

The purpose of this paper is to prove the existence, uniqueness and uniform convergence of the solutions of so-called projection nonconforming and mixed element methods and the equivalence between projection nonconforming element method and mixed element method with nonquasi-uniform partition for nonselfadjoint and inde®nite second order elliptic problems under minimal regularity assumption. Meanwhile, the optimal error estimate of the solution of mixed element method is obtained under H 2 smoothness hypothesis for nonselfadjoint and inde®nite elliptic problems without H 2 regularity. Finally, the discrete compactness result for nonconforming element space with nonquasi-uniform partition is proven, and some preconditioning methods for projection nonconforming and mixed element methods with nonquasi-uniform partition are given. It is proven that the H 1 -condition number of preconditioned operator is uniformly bounded and its singular values cluster in a relatively small ®nite interval.