Operator-splitting finite element algorithms for computations of high-dimensional parabolic problems

被引：14

作者：

Ganesan, Sashikumaar ^{[1
]}

Tobiska, Lutz ^{[2
]}

机构：

[1] Indian Inst Sci, Supercomp Educ & Res Ctr, Bangalore 560012, Karnataka, India

[2] Otto von Guericke Univ, Inst Anal & Numer Math, D-39016 Magdeburg, Germany

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 219卷 / 11期

关键词：

Operator-splitting method; Finite element method; Parabolic equations; High-dimensional problems; POPULATION BALANCE; NUMERICAL-SOLUTION; SIMULATION; CRYSTALLIZATION; FLOWS;

D O I：

10.1016/j.amc.2012.12.027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An operator-splitting finite element method for solving high-dimensional parabolic equations is presented. The stability and the error estimates are derived for the proposed numerical scheme. Furthermore, two variants of fully-practical operator-splitting finite element algorithms based on the quadrature points and the nodal points, respectively, are presented. Both the quadrature and the nodal point based operator-splitting algorithms are validated using a three-dimensional (3D) test problem. The numerical results obtained with the full 3D computations and the operator-split 2D + 1D computations are found to be in a good agreement with the analytical solution. Further, the optimal order of convergence is obtained in both variants of the operator-splitting algorithms. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：6182 / 6196

页数：15

共 22 条

[1] Finite element methods of an operator splitting applied to population balance equations [J].