一维双曲守恒律方程的基于指数多项式逼近的间断Petrov-Galerkin方法
A Discontinuous Petrov-Galerkin Method Based on Exponential Polynomial Approximation Spaces for One-Dimensional Hyperbolic Conservation Laws
摘要: 本文利用间断Petrov-Galerkin方法求解双曲守恒律方程，使用非代数多项式有限元空间(指数多项式基函数)来构造逼近函数进行空间离散，用SSP Runge-Kutta方法进行时间离散，TVB型minmod限制器用来抑制间断解数值计算时的数值振荡。通过对典型数值算例的计算，并与代数多项式间断Petrov-Galerkin方法的对比，结果显示本文的数值方法有良好的数值计算效果和数值稳定性。
Abstract: In this paper, a discontinuous Petrov-Galerkin method is used to solve the hyperbolic conservation laws. A non-algebraic polynomial finite element space, based on exponential polynomials, is used to construct the approximation function for spatial discretization. The SSP Runge-Kutta method is used for time discretization. The TVB minmod limiter is used to suppress the numerical oscillation in the numerical calculation of discontinuous solutions. Through the calculation of typical numerical examples and the comparison with algebraic polynomial discontinuous Petrov-Galerkin method, the results show that the numerical method in this paper has good numerical effect and numerical stability.
文章引用：孙雅洁, 高巍. 一维双曲守恒律方程的基于指数多项式逼近的间断Petrov-Galerkin方法[J]. 应用数学进展, 2021, 10(12): 4542-4553. https://doi.org/10.12677/AAM.2021.1012484

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