A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations
A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations
复制标题
非线性标量守恒方程的二阶极大值保拉格朗日有限元技术
DOI：
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发表时间：
2014
影响因子：
2.9
通讯作者：
Yong Yang
中科院分区：
文献类型：
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作者：
J. Guermond;Murtazo Nazarov;B. Popov;Yong Yang
本文提出了一种明确的（至少）二阶、满足最大原理的拉格朗日有限元方法来求解非线性标量守恒方程。该技术基于 Guermond 和 Nazarov 引入的新粘性双线性形式（Comput.Methods Appl.Mech.Engrg., 272 (2014), pp.198-213）、高阶熵粘性方法和 Boris-Book-Zalesak 通量校正技术。该算法适用于任何空间维度中的任意网格和所有 Lipschitz 通量。该方法的形式二阶精度及其收敛特性在一系列线性和非线性基准问题上进行了测试。
This paper proposes an explicit, (at least) second-order, maximum principle sat- isfying, Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a new viscous bilinear form introduced in Guermond and Nazarov (Com- put. Methods Appl. Mech. Engrg., 272 (2014), pp. 198-213), a high-order entropy viscosity method, and the Boris-Book-Zalesak flux correction technique. The algorithm works for arbitrary meshes in any space dimension and for all Lipschitz fluxes. The formal second-order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems.