Mixed Finite Element Methods for Diffusion Equations on Nonmatching Grids
نویسنده
چکیده
The hybridization technique is applied to replace the macro-hybrid mixed finite element problem for the diffusion equation by the equivalent cell-based formulation. The underlying algebraic system is condensed by eliminating the degrees of freedom which represent the interface flux and cell pressure variables to the system containing the Lagrange multipliers variables. An approach to the numerical solution of the condensed system is briefly discussed.
منابع مشابه
Mixed Finite Element Methods on Nonmatching Multiblock Grids
We consider mixed nite element methods for second order elliptic equations on non-matching multiblock grids. A mortar nite element space is introduced on the non-matching interfaces. We approximate in this mortar space the trace of the solution, and we impose weakly a continuity of ux condition. A standard mixed nite element method is used within the blocks. Optimal order convergence is shown f...
متن کاملMimetic finite difference methods for diffusion equations ∗
This paper reviews and extends the theory and application of mimetic finite difference methods for the solution of diffusion problems in strongly heterogeneous anisotropic materials. These difference operators satisfy the fundamental identities, conservation laws and theorems of vector and tensor calculus on nonorthogonal, nonsmooth, structured and unstructured computational grids. We provide e...
متن کاملPartition of unity method on nonmatching grids for the Stokes problem
We consider the Stokes problem on a plane polygonal domain Ω ⊂ R2 . We propose a finite element method for overlapping or nonmatching grids for the Stokes problem based on the partition of unity method. We prove that the discrete inf-sup condition holds with a constant independent of the overlapping size of the subdomains. The results are valid for multiple subdomains and any spatial dimension.
متن کاملA posteriori error estimates for mixed finite element and finite volume methods for problems coupled through a boundary with nonmatching grids
The primary purpose of this paper is to compare the accuracy and performance of two numerical approaches to solving systems of partial differential equations. These equations are posed on adjoining domains sharing boundary conditions on a common boundary interface in the important case when the meshes used on the two domains are nonmatching across the interface. The first, widely used approach ...
متن کاملA general framework for multigrid methods for mortar finite elements
In this paper, a general framework for the analysis of multigrid methods for mortar finite elements is considered. The numerical realization is based on the algebraic saddle point formulation arising from the discretization of second order elliptic equations on nonmatching grids. Suitable discrete Lagrange multipliers on the interface guarantee weak continuity and an optimal discretization sche...
متن کامل