Superconvergence of Finite Element Method for Parabolic Problem
نویسندگان
چکیده
We study superconvergence of a semi-discrete finite element scheme for parabolic problem. Our new scheme is based on introducing different approximation of initial condition. First, we give a superconvergence of uh −Rhu, then use a postprocessing to improve the accuracy to higher order.
منابع مشابه
Superconvergence of Fully Discrete Finite Elements for Parabolic Control Problems with Integral Constraints
A quadratic optimal control problem governed by parabolic equations with integral constraints is considered. A fully discrete finite element scheme is constructed for the optimal control problem, with finite elements for the spatial but the backward Euler method for the time discretisation. Some superconvergence results of the control, the state and the adjoint state are proved. Some numerical ...
متن کاملJ. KSIAM Vol.8, No.2, 23-38, 2004 SUPERCONVERGENCE OF FINITE ELEMENT METHODS FOR LINEAR QUASI-PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS
We consider finite element methods applied to a class of quasi parabolic integro-differential equations in R. Global strong superconvergence, which only requires that partitions are quasi-uniform, is investigated for the error between the approximate solution and the Sobolev-Volterra projection of the exact solution. Two order superconvergence results are demonstrated in W (Ω) and Lp(Ω), for 2 ...
متن کاملSuperconvergence of semidiscrete finite element methods for bilinear parabolic optimal control problems
In this paper, a semidiscrete finite element method for solving bilinear parabolic optimal control problems is considered. Firstly, we present a finite element approximation of the model problem. Secondly, we bring in some important intermediate variables and their error estimates. Thirdly, we derive a priori error estimates of the approximation scheme. Finally, we obtain the superconvergence b...
متن کاملA low order nonconforming anisotropic finite element approximation to parabolic problem
Ω fvdxdy. There have been a lot of work related to the finite element approximation to problem (1) in the framework of both semidiscrete and fully discrete schemes. For example, some superconvergence properties of conforming linear finite element (FE) were obtained by V. Thomeé with necessary help of Ritz projection and Lin Qun with a new analysis form, i.e., an analysis for the “short side” in...
متن کاملStrong Superconvergence of Finite Element Methods for Linear Parabolic Problems
We study the strong superconvergence of a semidiscrete finite element scheme for linear parabolic problems on Q Ω × 0, T , where Ω is a bounded domain in R d ≤ 4 with piecewise smooth boundary. We establish the global two order superconvergence results for the error between the approximate solution and the Ritz projection of the exact solution of ourmodel problem inW1,p Ω and Lp Q with 2 ≤ p < ...
متن کامل