共查询到20条相似文献,搜索用时 71 毫秒
1.
An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition. 相似文献
2.
Madhusmita Tripathy 《Applicable analysis》2013,92(4):855-868
The purpose of this article is to derive a posteriori error estimates for the H 1-Galerkin mixed finite element method for parabolic problems. We study both semidiscrete and fully discrete a posteriori error analyses using standard energy argument. A fully discrete a posteriori error analysis based on the backward Euler method is analysed and upper bounds for the errors are derived. The estimators yield upper bounds for the errors which are global in space and time. Our analysis is based on residual approach and the estimators are free from edge residuals. 相似文献
3.
CuiMing 《高校应用数学学报(英文版)》2001,16(3):297-303
Abstract. The operator-splitting methods for the mathematic model of one kind of oin reactionsfor the problem of groundwater are considered. Optimal error estimates in Lz and Hl norm areobtained for the approximation solution. 相似文献
4.
Madhusmita Tripathy 《Applicable analysis》2013,92(8):1213-1231
In this article, we study the semidiscrete H 1-Galerkin mixed finite element method for parabolic problems over rectangular partitions. The well-known optimal order error estimate in the L 2-norm for the flux is of order 𝒪(h k+1) (SIAM J. Numer. Anal. 35 (2), (1998), pp. 712–727), where k ≥ 1 is the order of the approximating polynomials employed in the Raviart–Thomas element. We derive a superconvergence estimate of order 𝒪(h k+3) between the H 1-Galerkin mixed finite element approximation and an appropriately defined local projection of the flux variable when k ≥ 1. A the new approximate solution for the flux with superconvergence of order 𝒪(h k+3) is realized via a postprocessing technique using local projection methods. 相似文献
5.
A nonconforming H^1-Calerkin mixed finite element method is analyzed for Sobolev equations on anisotropic meshes. The error estimates are obtained without using Ritz-Volterra projection. 相似文献
6.
7.
Summary Recently, Galerkin and collocation methods have been analyzed for boundary integral equation formulations of some potential problems in the plane with nonlinear boundary conditions, and stability results and error estimates in theH
1/2-norm have been proved (Ruotsalainen and Wendland, and Ruotsalainen and Saranen). We show that these results extend toL
p setting without any extra conditions. These extensions are proved by studying the uniform boundedness of the inverses of the linearized integral operators, and then considering the nonlinear equations. The fact that inH
1/2 setting the nonlinear operator is a homeomorphism with Lipschitz continuous inverse plays a crucial role. Optimal error estimates for the Galerkin and collocation method inL
p space then follow.This research was performed while the second author was visiting professor at the University of Delaware, spring 1989 相似文献
8.
In this paper, expanded mixed finite element methods for the initial-boundary-value problem of purely longitudinal motion equation of a homogeneous bar are proposed and analyzed. Optimal error estimates for the approximations of displacement in L2 norm and stress in H1 norm are obtained. 相似文献
9.
Devika Shylaja 《Numerical Methods for Partial Differential Equations》2020,36(5):972-997
The Hessian discretization method (HDM) for fourth-order linear elliptic equations provides a unified convergence analysis framework based on three properties namely coercivity, consistency, and limit-conformity. Some examples that fit in this approach include conforming and nonconforming finite element methods (ncFEMs), finite volume methods (FVMs) and methods based on gradient recovery operators. A generic error estimate has been established in L2, H1, and H2-like norms in literature. In this paper, we establish improved L2 and H1 error estimates in the framework of HDM and illustrate it on various schemes. Since an improved L2 estimate is not expected in general for FVM, a modified FVM is designed by changing the quadrature of the source term and a superconvergence result is proved for this modified FVM. In addition to the Adini ncFEM, in this paper, we show that the Morley ncFEM is an example of HDM. Numerical results that justify the theoretical results are also presented. 相似文献
10.
S. Arul Veda Manickam Kannan K. Moudgalya Amiya K. Pani 《Journal of Applied Mathematics and Computing》2004,15(1-2):1-28
We first apply a first order splitting to a semilinear reaction-diffusion equation and then discretize the resulting system by anH 1-Galerkin mixed finite element method in space. This semidiscrete method yields a system of differential algebraic equations (DAEs) ofindex one. Apriori error estimates for semidiscrete scheme are derived for both differential as well as algebraic components. For fully discretization, an implicit Runge-Kutta (IRK) methods is applied to the temporal direction and the error estimates are discussed for both components. Finally, we conclude the paper with a numerical example. 相似文献
11.
A new mixed scheme which combines the variation of constants and the H 1-Galerkin mixed finite element method is constructed for nonlinear Sobolev equation with nonlinear convection term. Optimal error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are given to confirm the theoretical analysis of the proposed method. 相似文献
12.
We study the convergence of H 1-Galerkin mixed finite element method for parabolic problems in one space dimension. Both semi-discrete and fully discrete schemes are analyzed assuming less regularity on initial data. More precisely, for the spatially discrete scheme, error estimates of order \(\mathcal{O}\) (h 2 t ?1/2) for positive time are established assuming the initial function p 0 ∈ H 2(Ω) ∩ H 0 1 (Ω). Further, we use energy technique together with parabolic duality argument to derive error estimates of order \(\mathcal{O}\) (h 2 t ?1) when p 0 is only in H 0 1 (Ω). A discrete-in-time backward Euler method is analyzed and almost optimal order error bounds are established. 相似文献
13.
Anita Hansbo 《BIT Numerical Mathematics》1991,31(4):664-685
In this paper we consider the numerical solution of a time-periodic linear parabolic problem. We derive optimal order error estimates inL
2() for approximate solutions obtained by discretizing in space by a Galerkin finite-element method and in time by single-step finite difference methods, using known estimates for the associated initial value problem. We generalize this approach and obtain error estimates for more general discretization methods in the norm of a Banach spaceB L
2(), e.g.,B=H
0
1
() orL
(). Finally, we consider some computational aspects and give a numerical example. 相似文献
14.
We propose and analyze a fully discrete H
1-Galerkin method with quadrature for nonlinear parabolic advection–diffusion–reaction equations that requires only linear
algebraic solvers. Our scheme applied to the special case heat equation is a fully discrete quadrature version of the least-squares
method. We prove second order convergence in time and optimal H
1 convergence in space for the computer implementable method. The results of numerical computations demonstrate optimal order
convergence of scheme in H
k
for k = 0, 1, 2.
Support of the Australian Research Council is gratefully acknowledged. 相似文献
15.
Nonconforming mixed finite element approximation to the stationary Navier-Stokes equations on anisotropic meshes 总被引:1,自引:0,他引:1
The main aim of this paper is to study the error estimates of a rectangular nonconforming finite element for the stationary Navier-Stokes equations under anisotropic meshes. That is, the nonconforming rectangular element is taken as approximation space for the velocity and the piecewise constant element for the pressure. The convergence analysis is presented and the optimal error estimates both in a broken H1-norm for the velocity and in an L2-norm for the pressure are derived on anisotropic meshes. 相似文献
16.
四阶强阻尼波方程的新混合元方法 总被引:4,自引:3,他引:4
构造半线性四阶强阻尼波动方程的新H1-Galerkin混合有限元方法,得到一维情况下半离散和全离散格式最优收敛阶误差估计,并且推广到二维和三维情况,不用验证LBB相容性条件. 相似文献
17.
P. P. B. Eggermont 《Numerische Mathematik》1992,62(1):35-48
Summary We analyze the quadrature error associated with operational quadrature methods for convolution equations. The assumptions are that the convolution kernel is inL
1 and that its Laplace transform is analytic and bounded in an obtuse sector of the complex plane. Under these circumstances the Laplace transform has a slow variation property which admits a Fourier analysis of the quadrature error. We provide generalL
p
error estimates assuming suitable smoothness conditions on the function under convolution. 相似文献
18.
Bhupen Deka 《Journal of Computational and Applied Mathematics》2010,234(2):605-612
The purpose of this paper is to study the effect of the numerical quadrature on the finite element approximation to the exact solution of elliptic equations with discontinuous coefficients. Due to low global regularity of the solution, it seems difficult to achieve optimal order of convergence with classical finite element methods [Z. Chen, J. Zou, Finite element methods and their convergence for elliptic and parabolic interface problems, Numer. Math. 79 (1998) 175-202]. We derive error estimates in finite element method with quadrature for elliptic interface problems in a two-dimensional convex polygonal domain. Optimal order error estimates in L2 and H1 norms are shown to hold even if the regularity of the solution is low on the whole domain. Finally, numerical experiment for two dimensional test problem is presented in support of our theoretical findings. 相似文献
19.
Optimal order error estimates in H
1, for the Q
1 isoparametric interpolation were obtained in Acosta and Durán (SIAM J Numer Anal37, 18–36, 1999) for a very general class of degenerate convex quadrilateral elements. In this work we show that the same conlusions are valid in W
1,p
for 1≤ p < 3 and we give a counterexample for the case p ≥ 3, showing that the result cannot be generalized for more regular functions. Despite this fact, we show that optimal order error estimates are valid for any p ≥ 1, keeping the interior angles of the element bounded away from 0 and π, independently of the aspect ratio. We also show that the restriction on the maximum angle is sharp for p ≥ 3. 相似文献
20.
Zhiqiang Cai 《Numerische Mathematik》1990,58(1):713-735
Summary The finite volume element method (FVE) is a discretization technique for partial differential equations. It uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations, then restricts the admissible functions to a finite element space to discretize the solution. this paper develops discretization error estimates for general selfadjoint elliptic boundary value problems with FVE based on triangulations with linear finite element spaces and a general type of control volume. We establishO(h) estimates of the error in a discreteH
1 semi-norm. Under an additional assumption of local uniformity of the triangulation the estimate is improved toO(h
2). Results on the effects of numerical integration are also included.This research was sponsored in part by the Air Force Office of Scientific Research under grant number AFOSR-86-0126 and the National Science Foundation under grant number DMS-8704169. This work was performed while the author was at the University of Colorado at Denver 相似文献