Error estimates for least-squares mixed finite elements
نویسندگان
چکیده
A least-squar es mixed finite element method is formulated and applied foi a c lass of second ofdei elhptic problems in two and three dimensionaï domains The pi imaty solution u and the flux a are approximated usmg finite element spaces consisting of piecewise polynomials of de grée k and r respectively The method is nonconforming in the sensé that the boundary condition for the flux approximation cannot be satisfied exactly on the whole boundary F— so it is satisfied only at the nodes on F Optimal Land H-error estimâtes are denved under the standard regulanty assumption on the finite element partition (the UBfè-condition is not requued) The important cases ofk — i and k + l — r are considered
منابع مشابه
An adaptive least-squares mixed finite element method for pseudo-parabolic integro-differential equations
In this article, an adaptive least-squares mixed finite element method is studied for pseudo-parabolic integro-differential equations. The solutions of least-squares mixed weak formulation and mixed finite element are proved. A posteriori error estimator is constructed based on the least-squares functional and the posteriori errors are obtained. Keywords—Pseudo-parabolic integro-differential eq...
متن کاملLeast-Squares Methods for Elasticity with Weakly Imposed Symmetry
The related physical equations of linear elasticity are the equilibrium equation and the constitutive equation, which expresses a relation between the stress and strain tensors. This is a first-order partial differential system such that a least squares method based on a stress-displacement formulation can be used whose corresponding finite element approximation does not preserve the symmetry o...
متن کاملError Analysis for Constrained First-Order System Least-Squares Finite-Element Methods
In this paper, a general error analysis is provided for finite-element discretizations of partial differential equations in a saddle-point form with divergence constraint. In particular, this extends upon the work of [J. H. Adler and P. S. Vassilevski, Springer Proc. Math. Statist. 45, Springer, New York, 2013, pp. 1–19], giving a general error estimate for finite-element problems augmented wit...
متن کاملAn augmented mixed finite element method for the vorticity–velocity–pressure formulation of the Stokes equations
This paper deals with the numerical approximation of the stationary two-dimensional Stokes equations, formulated in terms of vorticity, velocity and pressure, with non-standard boundary conditions. Here, by introducing a Galerkin least-squares term, we end up with a stabilized variational formulation that can be recast as a twofold saddle point problem. We propose two families of mixed finite e...
متن کاملSuperconvergence of Least-squares Mixed Finite Elements
In this paper we consider superconvergence and supercloseness in the least-squares mixed finite element method for elliptic problems. The supercloseness is with respect to the standard and mixed finite element approximations of the same elliptic problem, and does not depend on the properties of the mesh. As an application, we will derive more precise a priori bounds for the least squares mixed ...
متن کامل