Numerical analysis of a least-squares finite element method for the time-dependent advection-diffusion equation

被引：8
作者：
Leal Toledo, R. C. [2 ,3 ]
Ruas, V. [1 ,3 ]
机构：
[1] UPMC Univ Paris 6, UMR 7190, Inst Jean Rond dAlembert, CNRS, Paris, France
[2] Univ Fed Fluminense, Dept Ciencia Comp, Niteroi, RJ, Brazil
[3] Univ Fed Fluminense, Programa Posgrad Ciencia Comp, Niteroi, RJ, Brazil
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2011年 / 235卷 / 12期
关键词：
Advection-diffusion; Crank-Nicholson; Finite elements; Least squares; Reaction; Time-dependent; 2ND-ORDER ELLIPTIC PROBLEMS; FLOW;
D O I：
10.1016/j.cam.2011.02.022
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A mixed finite element scheme designed for solving the time-dependent advection-diffusion equations expressed in terms of both the primal unknown and its flux, incorporating or not a reaction term, is studied. Once a time discretization of the Crank-Nicholson type is performed, the resulting system of equations allows for a stable approximation of both fields, by means of classical Lagrange continuous piecewise polynomial functions of arbitrary degree, in any space dimension. Convergence in the norm of H-1 x H(div) in space and in appropriate senses in time applying to this pair of fields is demonstrated. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码：3615 / 3631
页数：17
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