Superconvergence for the Gradient of Finite Element Approximations by L Projections∗
نویسندگان
چکیده
A gradient recovery technique is proposed and analyzed for finite element solutions which provides new gradient approximations with high order of accuracy. The recovery technique is based on the method of least-squares surface fitting in a finite-dimensional space corresponding to a coarse mesh. It is proved that the recovered gradient has a high order of superconvergence for appropriately chosen surface fitting spaces. The recovery technique is robust, efficient, and applicable to a wide class of problems such as the Stokes and elasticity equations.
منابع مشابه
A Superconvergent Finite Element Scheme for the Reissner-mindlin Plate by Projection Methods
The Reissner-Mindlin model is frequently used by engineers for plates and shells of small to moderate thickness. This model is well known for its “locking” phenomenon so that many numerical approximations behave poorly when the thickness parameter tends to zero. Following the formulation derived by Brezzi and Fortin, we construct a new finite element scheme for the Reissner-Mindlin model using ...
متن کاملExpanded mixed finite element methods for linear second-order elliptic problems, I
We develop a new mixed formulation for the numencal solution of second-order elliptic problems This new formulation expands the standard mixed formulation in the sense that three variables are exphcitly treated the scalar unknown, its gradient, and its flux (the coefficient times the gradient) Based on this formulation, mixed finite element approximations of the second-order elliptic problems a...
متن کاملA weak Galerkin finite element method for second-order elliptic problems
In this paper, authors shall introduce a finite element method by using a weakly defined gradient operator over discontinuous functions with heterogeneous properties. The use of weak gradients and their approximations results in a new concept called discrete weak gradients which is expected to play important roles in numerical methods for partial differential equations. This article intends to ...
متن کاملSuperconvergence and Gradient Recovery of Linear Finite Elements for the Laplace-Beltrami Operator on General Surfaces
Superconvergence results and several gradient recovery methods of finite element methods in flat spaces are generalized to the surface linear finite element method for the LaplaceBeltrami equation on general surfaces with mildly structured triangular meshes. For a large class of practically useful grids, the surface linear finite element solution is proven to be superclose to an interpolant of ...
متن کامل