论文标题
1D线性双曲方程的两种类型的光谱体积方法具有变性变量系数
Two types of spectral volume methods for 1-D linear hyperbolic equations with degenerate variable coefficients
论文作者
论文摘要
在本文中，我们分析了具有变性可变系数的一维双曲方程的两类光谱体积（SV）方法。两类的SV方法是通过让分段$ k $ -th订单（$ k \ ge 1 $是一个任意整数）的多项式函数来构建的。在每个{\ it控制量}中，通过将基础网状的间隔元素与$ k $ gauss-gauss-legendre points（lsv）或rada（lsv）分开来满足本地保护定律。对于一般的非均匀网格，对两种方法的$ l^2 $ norm稳定性和最佳订单收敛属性都被严格证明。还已经研究了两个SV方案的超授权行为：证明，在$ l^2 $ norm中，SV通量函数近似于$（k+2）$ - TH订单的确切通量，而SV解决方案近似于$（k+\ frac32）$ - ther ofer off acker lux lux;还发现并证明了某些特殊点和元素平均值的某些超级融合行为。我们的理论发现通过几个数值实验验证。
In this paper, we analyze two classes of spectral volume (SV) methods for one-dimensional hyperbolic equations with degenerate variable coefficients. The two classes of SV methods are constructed by letting a piecewise $k$-th order ($k\ge 1$ is an arbitrary integer) polynomial function satisfy the local conservation law in each {\it control volume} obtained by dividing the interval element of the underlying mesh with $k$ Gauss-Legendre points (LSV) or Radaus points (RSV). The $L^2$-norm stability and optimal order convergence properties for both methods are rigorously proved for general non-uniform meshes. The superconvergence behaviors of the two SV schemes have been also investigated: it is proved that under the $L^2$ norm, the SV flux function approximates the exact flux with $(k+2)$-th order and the SV solution approximates the exact solution with $(k+\frac32)$-th order; some superconvergence behaviors at certain special points and for element averages have been also discovered and proved. Our theoretical findings are verified by several numerical experiments.
