Convergence Analysis of a Non-Overlapping Domain Decomposition Method for Elliptic PDEs
نویسندگان
چکیده
In this study we analyze a non-overlapping domain decomposition method for the solution of elliptic Partial Di erential Equation (PDE) problems. This domain decomposition method involves the solution of Dirichlet and Neumann PDE problems on each subdomain, coupled with smoothing operations on the interfaces of the subdomains. The convergence analysis of the method at the di erential equation level is presented. The numerical results con rm the theoretical ones and exhibit computational e ciency of the method.
منابع مشابه
A Robin-robin Non-overlapping Domain Decomposition Method for an Elliptic Boundary Control Problem
A Robin-Robin non-overlapping domain decomposition method for an optimal boundary control problem associated with an elliptic boundary value problem is presented. The existence of the whole domain and subdomain optimal solutions is proven. The convergence of the subdomain optimal solutions to the whole domain optimal solution is shown. The optimality system is derived and a gradient-type method...
متن کاملMaximum norm error analysis of a nonmatching grids finite element method for linear elliptic PDEs
Keywords: Elliptic PDEs Schwarz alternating method Nonmatching grids Finite element L 1 – error estimate a b s t r a c t In this paper, we study a nonmatching grid finite element approximation of linear elliptic PDEs in the context of the Schwarz alternating domain decomposition.We show that the approximation converges optimally in the maximum norm, on each subdomain, making use of the geometri...
متن کاملAnalysis of a Non{overlapping Domain Decomposition Method for Elliptic Partial Diierential Equations 1
In this study we analyze a non-overlapping domain decomposition method for the solution of elliptic Partial Diierential Equation (PDE) problems. This domain decomposition method involves the solution of Dirichlet and Neumann PDE problems on each subdomain, coupled with smoothing operations on the interfaces of the subdomains. The convergence analysis of the method at the diierential equation le...
متن کاملConvergence estimates for multigrid algorithms with SSC smoothers and applications to overlapping domain decomposition
In this paper we study convergence estimates for a multigrid algorithm with smoothers of successive subspace correction (SSC) type, applied to symmetric elliptic PDEs. First, we revisit a general convergence analysis on a class of multigrid algorithms in a fairly general setting, where no regularity assumptions are made on the solution. In this framework, we are able to explicitly highlight the...
متن کاملOverlapping Additive Schwarz Preconditioners for Elliptic Pdes on the Unit Sphere
We present an overlapping domain decomposition technique for solving elliptic partial differential equations on the sphere. The approximate solution is constructed using shifts of a strictly positive definite kernel on the sphere. The condition number of the Schwarz operator depends on the way we decompose the scattered set into smaller subsets. The method is illustrated by numerical experiment...
متن کامل