Primal Hybrid Finite Element Methods for 2nd Order Elliptic Equations
نویسندگان
چکیده
The paper is devoted to the construction of finite element methods for 2nd order elliptic equations based on a primal hybrid variational principle. Optimal error bounds are proved. As a corollary, we obtain a general analysis of nonconforming finite element methods.
منابع مشابه
On the Use of Lagrange Multipliers in Domain Decomposition for Solving Elliptic Problems
The primal hybrid method for solving second-order elliptic equations is extended from finite element approximations to general bases. Variational techniques are used to show convergence of approximations to the solution of the homogeneous Dirichlet problem for selfadjoint equations. Error estimates are obtained and examples are given. Introduction Lagrange multipliers have been employed to defi...
متن کاملA family of Multiscale Hybrid-Mixed finite element methods for the Darcy equation with rough coefficients
We aim at proposing novel stable finite element methods for the mixed Darcy equation with heterogeneous coefficients within a space splitting framework. We start from the primal hybrid formulation of the elliptic model for the pressure. Localization of this infinite-dimensional problem leads to element-level boundary value problems which embed multiscale and high-contrast features in a natural ...
متن کاملInterior Methods For a Class of Elliptic Variational Inequalities
We consider the application of primal-dual interior methods to the optimization of systems arising in the finite-element discretization of a class of elliptic variational inequalities. These problems lead to very large (possibly non-convex) optimization problems with upper and lower bound constraints. When interior methods are applied to the discretized problem, the resulting linear systems hav...
متن کاملSome a Priori Error Estimates for Finite Element Approximations of Elliptic and Parabolic Linear Stochastic Partial Differential Equations
We study some theoretical aspects of Legendre polynomial chaos based finite element approximations of elliptic and parabolic linear stochastic partial differential equations (SPDEs) and provide a priori error estimates in tensor product Sobolev spaces that hold under appropriate regularity assumptions. Our analysis takes place in the setting of finitedimensional noise, where the SPDE coefficien...
متن کاملA deluxe FETI-DP algorithm for a hybrid staggered discontinuous Galerkin method for H(curl)-elliptic problems
Convergence theories and a deluxe dual and primal finite element tearing and interconnecting algorithm are developed for a hybrid staggered DG finite element approximation of H(curl) elliptic problems in two dimensions. In addition to the advantages of staggered DG methods, the basis functions of the new hybrid staggered DG method are all locally supported in the triangular elements, and a Lagr...
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 2010