An Optimal-Order Multigrid Method for PI Nonconforming Finite Elements
نویسندگان
چکیده
An optimal-order multigrid method for solving second-order elliptic boundary value problems using PI nonconforming finite elements is developed.
منابع مشابه
A Nonconforming Multigrid Method for the Stationary Stokes Equations
An optimal-order W-cycle multigrid method for solving the stationary Stokes equations is developed, using PI nonconforming divergence-free finite elements.
متن کاملOn the Implementation of Mixed Methods as Nonconforming Methods for Second-order Elliptic Problems
In this paper we show that mixed finite element methods for a fairly general second-order elliptic problem with variable coefficients can be given a nonmixed formulation. (Lower-order terms are treated, so our results apply also to parabolic equations.) We define an approximation method by incorporating some projection operators within a standard Galerkin method, which we call a projection fini...
متن کاملLocal Multilevel Methods for Adaptive Nonconforming Finite Element Methods
In this paper, we propose a local multilevel product algorithm and its additive version for linear systems arising from adaptive nonconforming finite element approximations of second order elliptic boundary value problems. The abstract Schwarz theory is applied to analyze the multilevel methods with Jacobi or Gauss-Seidel smoothers performed on local nodes on coarse meshes and global nodes on t...
متن کاملMultigrid and multilevel methods for nonconforming Q1 elements
In this paper we study theoretical properties of multigrid algorithms and multilevel preconditioners for discretizations of second-order elliptic problems using nonconforming rotated Q1 finite elements in two space dimensions. In particular, for the case of square partitions and the Laplacian we derive properties of the associated intergrid transfer operators which allow us to prove convergence...
متن کاملNew robust nonconforming finite elements of higher order
We study second order nonconforming finite elements as members of a new family of higher order approaches which behave optimally not only on multilevel refined grids, but also on perturbed grids which are still shape regular but which consist no longer of asymptotically affine equivalent mesh cells. We present two approaches to prevent this order reduction: The first one is based on the use of ...
متن کامل