守恒定律
间断伽辽金法
数学
投影(关系代数)
有限元法
标量(数学)
非线性系统
有界函数
应用数学
伽辽金法
数学分析
几何学
算法
物理
热力学
量子力学
作者
Bernardo Cockburn,San‐Yih Lin,Chi‐Wang Shu
标识
DOI:10.1016/0021-9991(89)90183-6
摘要
This is the third paper in a series in which we construct and analyze a class of TVB (total variation bounded) discontinuous Galerkin finite element methods for solving conservation laws ut+Σi=1d(fi(u)xi=0. In this paper we present the method in a system of equations, stressing the point of how to use the weak form in the component spaces, but to use the local projection limiting in the characteristic fields, and how to implement boundary conditions. A 1-dimensional system is thus chosen as a model. Different implementation techniques are discussed, theories analogous to scalar cases are proven for linear systems, and numerical results are given illustrating the method on nonlinear systems. Discussions of handling complicated geometries via adaptive triangle elements will appear in future papers.
科研通智能强力驱动
Strongly Powered by AbleSci AI