Overlapping Nonmatching Grid Mortar Element Methods for Elliptic Problems
نویسندگان
چکیده
In the first part of the paper, we introduce an overlapping mortar finite element method for solving two-dimensional elliptic problems discretized on overlapping nonmatching grids. We prove an optimal error bound and estimate the condition numbers of certain overlapping Schwarz preconditioned systems for the two-subdomain case. We show that the error bound is independent of the size of the overlap and the ratio of the mesh parameters. In the second part, we introduce three additive Schwarz preconditioned conjugate gradient algorithms based on the trivial and harmonic extensions. We provide estimates for the spectral bounds on the condition numbers of the preconditioned operators. We show that although the error bound is independent of the size of the overlap, the condition number does depend on it. Numerical examples are presented to support our theory.
منابع مشابه
A FETI-DP Preconditioner with A Special Scaling for Mortar Discretization of Elliptic Problems with Discontinuous Coefficients
We consider two-dimensional elliptic problems with discontinuous coefficients discretized by the finite element method on geometrically conforming nonmatching triangulations across the interface using the mortar technique. The resulting discrete problem is solved by a dual-primal FETI method. In this paper we introduce and analyze a preconditioner with a special scaling of coefficients and step...
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 کاملA Non-mortar Mixed Finite Element Method for Elliptic Problems on Non-matching Multiblock Grids a Non-mortar Mixed Finite Element Method for Elliptic Problems on Non-matching Multiblock Grids 1
We consider the approximation of second order elliptic equations on domains that can be described as a union of sub-domains or blocks. We assume that a grid is deened on each block independently, so that the resulting grid over the entire domain need not be conforming (i.e., match) across the block boundaries. Several techniques have been developed to approximate elliptic equations on multibloc...
متن کاملNeumann–neumann Algorithms for a Mortar Crouzeix–raviart Element for 2nd Order Elliptic Problems
The paper proposes two scalable variants of the Neumann–Neumann algorithm for the lowest order Crouzeix–Raviart finite element or the nonconforming P1 finite element on nonmatching meshes. The overall discretization is done using a mortar technique which is based on the application of an approximate matching condition for the discrete functions, requiring function values only at the mesh interf...
متن کاملAdditive Schwarz methods for the Crouzeix-Raviart mortar finite element for elliptic problems with discontinuous coefficients
In this paper, we propose two variants of the additive Schwarz method for the approximation of second order elliptic boundary value problems with discontinuous coefficients, on nonmatching grids using the lowest order Crouzeix-Raviart element for the discretization in each subdomain. The overall discretization is based on the mortar technique for coupling nonmatching grids. The convergence beha...
متن کامل