Finite Element Methods for Biharmonic Problem
نویسندگان
چکیده
and Applied Analysis 3 Let EI and EB be the set of interior edges and boundary edges of Th, respectively. Let E EI ∪ EB. Denote by v the restriction of v to Ki. Let e eij ∈ EI with i > j. Then we denote the jump v and the average {v} of v on e by v |e v ∣ ∣ ∣ e −v ∣ ∣ ∣ e , {v}|e 1 2 ( v ∣ ∣ ∣ e v ∣ ∣ ∣ e ) . 2.4 If e ei ∈ EB, we denote v and {v} of v on e by v |e {v}|e v ∣ ∣ ∣ e . 2.5
منابع مشابه
A 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 of a Quadrature Finite Element Galerkin Scheme for a Biharmonic Problem
A quadrature finite element Galerkin scheme for a Dirichlet boundary value problem for the biharmonic equation is analyzed for a solution existence, uniqueness, and convergence. Conforming finite element space of Bogner-Fox-Schmit rectangles and an integration rule based on the two-point Gaussian quadrature are used to formulate the discrete problem. An H2-norm error estimate is obtained for th...
متن کاملMultigrid Methods for the Biharmonic Problem Discretized by Conforming 1 Finite Elements on Nonnested Meshes
Abstract. We consider multigrid algorithms for the biharmonic problem discretized by conforming 1 finite elements. Most finite elements for the biharmonic equation are nonnested in the sense that the coarse finite element space is not a subspace of the space of similar elements defined on a refined mesh. To define multigrid methods, certain intergrid transfer operators have to be constructed. W...
متن کاملMultigrid Methods for a Biharmonic Problem with Boundary Conditions of the Cahn-Hilliard Type
We present multigrid methods for a biharmonic problem with boundary conditions of the Cahn-Hilliard type. These multigrid methods are based on discretizations obtained by a quadratic C interior penalty method. Since the finite element space is a standard space for second order problems, multigrid solves for second order problems can be used naturally in the smoothing steps. We will present theo...
متن کاملFinite Element Methods for Elliptic Equations Using Nonconforming Elements
A finite element method is developed for approximating the solution of the Dirichlet problem for the biharmonic operator, as a canonical example of a higher order elliptic boundary value problem. The solution is approximated by special choices of classes of discontinuous functions, piecewise polynomial functions, by virtue of a special variational formulation of the boundary value problem. The ...
متن کاملA Black-Box Multigrid Preconditioner for the Biharmonic Equation
We examine the convergence characteristics of a preconditioned Krylov subspace solver applied to the linear systems arising from low-order mixed finite element approximation of the biharmonic problem. The key feature of our approach is that the preconditioning can be realized using any “black-box” multigrid solver designed for the discrete Dirichlet Laplacian operator. This leads to preconditio...
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:
دوره شماره
صفحات -
تاریخ انتشار 2014