Abstract
We consider the Dirichlet problem for an elliptic equation with a singularity. The singularity of the solution to the problem is caused by the presence of a re-entrant corner at the boundary of the domain. We define an Rν-generalized solution for this problem. This allows for the construction of numerical methods for finding an approximate solution without loss of accuracy. In this paper, the existence and uniqueness of the Rν-generalized solution in set W∘2,α1(Ω,δ) is proven. The Rν-generalized solution is the same for different parameters ν.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference24 articles.
1. The Finite Element Method for Elliptic Problems;Ciarlet,1978
2. Finite Difference Schemes for Differential Equations with Generalized Solutions;Samarskii,1987
3. Approximation of Solutions of Mixed Boundary Value Problems for Poisson's Equation by Finite Differences
4. Higher-order Rayleigh-Ritz approximations;Fix;J. Math. Mech.,1969
5. Elliptic Problems in Nonsmooth Domains;Grisvard,1985
Cited by
17 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献