A priori error estimates of a combined mixed finite element and local discontinuous Galerkin method for an incompressible miscible displacement problem

被引：4
作者：
Yang, Jiming [1 ,2 ]
Chen, Yanping [3 ]
Huang, Yunqing [4 ]
机构：
[1] Xiangtan Univ, Coll Civil Engn & Mech, Xiangtan 411105, Peoples R China
[2] Hunan Inst Engn, Coll Sci, Xiangtan 411104, Peoples R China
[3] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
[4] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 334卷
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
A priori error; Mixed finite element; Local discontinuous Galerkin; Miscible displacement problems; CONSERVATION-LAWS; APPROXIMATION; DIFFUSION;
D O I：
10.1016/j.amc.2017.12.022
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A numerical approximation for a kind of incompressible miscible displacement problems in high dimension in porous media is studied. Mixed finite element method is applied to the flow equation, and the transport one is solved by the local discontinuous Galerkin method (LDG). Based on interpolation projection properties and the induction hypothesis, a priori hp error estimates are obtained. Numerical results are presented, which verify the theoretical results. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：141 / 151
页数：11
相关论文
共 29 条
[1]   The local discontinuous Galerkin method for contaminant transport [J].
Aizinger, V ;
Dawson, C ;
Cockburn, B ;
Castillo, P .
ADVANCES IN WATER RESOURCES, 2000, 24 (01) :73-87
[2]   THE OPTIMAL CONVERGENCE RATE OF THE P-VERSION OF THE FINITE-ELEMENT METHOD [J].
BABUSKA, I ;
SURI, M .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1987, 24 (04) :750-776
[3]  
BABUSKA I, 1987, RAIRO-MATH MODEL NUM, V21, P199
[4]   A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations [J].
Bassi, F ;
Rebay, S .
JOURNAL OF COMPUTATIONAL PHYSICS, 1997, 131 (02) :267-279
[5]  
BREZZI F, 1987, RAIRO-MATH MODEL NUM, V21, P581
[6]   An A posteriori error estimate for the local discontinuous Galerkin method applied to linear and nonlinear diffusion problems [J].
Bustinza, R ;
Gatica, GN ;
Cockburn, B .
JOURNAL OF SCIENTIFIC COMPUTING, 2005, 22-3 (01) :147-185
[7]   Performance of discontinuous Galerkin methods for elliptic PDEs [J].
Castillo, P .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2002, 24 (02) :524-547
[8]   Local discontinuous Galerkin methods for elliptic problems [J].
Castillo, P ;
Cockburn, B ;
Perugia, I ;
Schötzau, D .
COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING, 2002, 18 (01) :69-75
[9]  
Cheng A., 1995, NUMER MATH, V4, P222
[10]   The local discontinuous Galerkin method for time-dependent convection-diffusion systems [J].
Cockburn, B ;
Shu, CW .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1998, 35 (06) :2440-2463
123