The Ciarlet-Raviart Method for Biharmonic Problems on General Polygonal Domains: Mapping Properties and Preconditioning
نویسنده
چکیده
For biharmonic boundary value problems, the Ciarlet-Raviart mixed method is considered on polygonal domains without additional convexity assumptions. Mapping properties of the involved operators on the continuous as well as on the discrete level are studied. Based on this, efficient preconditioners are constructed and numerical experiments are shown.
منابع مشابه
Multigrid Preconditioning for the Biharmonic Dirichlet Problem
A multigrid preconditioning scheme for solving the Ciarlet-Raviart mixed method equations for the biharmonic Dirichlet problem is presented. In particular, a Schur complement formulation for these equations which yields non-inherited quadratic forms is considered. The preconditioning scheme is compared with a standard W-cycle multigrid iteration. It is proved that a Variable V-cycle preconditio...
متن کاملC IPG Method for Biharmonic Eigenvalue Problems
We investigate the C interior penalty Galerkin (C IPG) method for biharmonic eigenvalue problems with the boundary conditions of the clamped plate, the simply supported plate and the Cahn-Hilliard type. We prove the convergence of the method and present numerical results to illustrate its performance. We also compare the C IPG method with the Argyris C finite element method, the Ciarlet-Raviart...
متن کاملRemarks on the Ciarlet-raviart Mixed Finite Element
Abstract. This paper derives a new scheme for the mixed finite element method for the biharmonic equation in which the flow function is approximated by piecewise quadratic polynomial and vortex function by piecewise linear polynomials. Assuming that the partition, with triangles as elements, is quasi-uniform, then the proposed scheme can achieve the approximation order that is observed by the C...
متن کاملA Mixed Finite Element Method for the Biharmonic Problem Using Biorthogonal or Quasi-Biorthogonal Systems
We consider a finite element method based on biorthogonal or quasi-biorthogonal systems for the biharmonic problem. The method is based on the primal mixed finite element method due to Ciarlet and Raviart for the biharmonic equation. Using different finite element spaces for the stream function and vorticity, this approach leads to a formulation only based on the stream function. We prove optim...
متن کاملConvergence Analysis and Comparison of the H- and P- Extensions with Mixed Finite Element
A mixed formulation with two main variables, based on the Ciarlet-Raviart technique, with 0 C continuity shape functions is employed for the solution of some types of biharmonic equations in 1-D. The continuous and discrete Babuška-Brezzi inf-sup conditions are established. The formulation is numerically tested for both the hand pextensions. The model problems involve the standard biharmonic eq...
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:
- SIAM J. Numerical Analysis
دوره 53 شماره
صفحات -
تاریخ انتشار 2015