A mass-conservative characteristic FE scheme for optimal control problems governed by convection-diffusion equations

被引：5

作者：

Fu, Hongfei ^{[2
]}

Rui, Hongxing ^{[1
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

[2] China Univ Petr, Dept Computat & Appl Math, Qingdao 266580, Peoples R China

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2012年 / 241卷

基金：

中国国家自然科学基金;

关键词：

Mass-conservative characteristic finite element; Optimal control problems; Convection-diffusion equations; A priori error estimates; FINITE-ELEMENT; EDGE STABILIZATION; GALERKIN METHOD; A-PRIORI; ADVECTION;

D O I：

10.1016/j.cma.2012.05.019

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we develop a mass-conservative characteristic finite element scheme for optimal control problems governed by linear singularly perturbed, convection-diffusion equations. We discuss the case that the velocity fields are non-divergence-free. The space discretization of the state variable is done by piecewise linear continuous functions, whereas the control variable is approximated by piecewise constant functions due to the limitation of the regularity. The scheme preserves the mass balance for the original state equation. We derive a priori error estimates for both the control and state approximations. Some numerical examples are presented to show the efficiency of the proposed scheme. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：82 / 92

页数：11

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