Partition of unity method on nonmatching grids for the Stokes problem
نویسندگان
چکیده
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.
منابع مشابه
A conforming finite element method for overlapping and nonmatching grids
In this paper we propose a finite element method for nonmatching overlapping grids based on the partition of unity. Both overlapping and nonoverlapping cases are considered. We prove that the new method admits an optimal convergence rate. The error bounds are in terms of local mesh sizes and they depend on neither the overlapping size of the subdomains nor the ratio of the mesh sizes from diffe...
متن کاملNotes on the Schwartz Alternating Method for Partition of Unity FEM
We consider discretization on overlapping non-matching grids for elliptic equations by using the Schwartz alternating (SA) method. We investigate also the dependence between the angle of partition of unity (PU) subspaces and the condition number of the stiffness matrix for a model problem. The aim of the paper is to find strategies to choose optimal or quasi-optimal partition of unity set of fu...
متن کاملA FETI-DP Formulation for Two-dimensional Stokes Problem on Nonmatching Grids
We consider a FETI-DP formulation of the Stokes problem with mortar methods. To solve the Stokes problem correctly and efficiently, redundant continuity constraints are introduced. Lagrange multipliers corresponding to the redundant constraints are treated as primal variables in the FETI-DP formulation. We propose a preconditioner for the FETI-DP operator and show that the condition number of t...
متن کاملLocal and Parallel Finite Element Algorithms Based on the Partition of Unity for the Stokes Problem
By combining the techniques of two-grid method and the partition of unity, two local and parallel finite element algorithms are presented for the Stokes problem. The most interesting features of these algorithms are: (1) the partition of unity technique introduces a framework for domain decomposition, (2) only a series of local residual problems need to be solved on these subdomains in parallel...
متن کاملMaximum Norm Analysis of an Overlapping Nonmatching Grids Method Forthe Obstacle Problem
We provide a maximum norm analysis of an overlapping Schwarz method on nonmatching grids for second-order elliptic obstacle problem. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The grid points on the subdomain boundaries need not match the grid points from the other subdomain. Under a discrete maximum princ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Num. Math.
دوره 13 شماره
صفحات -
تاریخ انتشار 2005