A monotonicity preserving, nonlinear, finite element upwind method for the transport equation

被引：10

作者：

Burman, Erik ^{[1
]}

机构：

[1] Univ London Univ Coll, Dept Math, London WC1E 6BT, England

来源：

APPLIED MATHEMATICS LETTERS | 2015年 / 49卷

基金：

英国工程与自然科学研究理事会;

关键词：

Stabilized finite element method; Shock capturing; Flux correction; Monotonicity preserving; Transport equation; DISCRETE MAXIMUM PRINCIPLE;

D O I：

10.1016/j.aml.2015.05.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a simple upwind finite element method that is monotonicity preserving and weakly consistent of order O(h(3/2)). The scheme is nonlinear, but since an explicit time integration method is used the added cost due to the nonlinearity is not prohibitive. We prove the monotonicity preserving property for the forward Euler method and for a second order Runge Kutta method. The convergence properties of the Runge Kutta finite element method are verified on a numerical example. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：141 / 146

页数：6

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