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首页> 外文期刊>SIAM Journal on Numerical Analysis >ARBITRARY LAGRANGIAN-EULERIAN DISCONTINUOUS GALERKIN METHOD FOR HYPERBOLIC EQUATIONS INVOLVING delta-SINGULARITIES
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ARBITRARY LAGRANGIAN-EULERIAN DISCONTINUOUS GALERKIN METHOD FOR HYPERBOLIC EQUATIONS INVOLVING delta-SINGULARITIES

机译:涉及三角形奇异性的双曲线方程的任意拉格朗日 - 欧拉·欧拉欧利亚

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摘要

In this paper, we develop and analyze an arbitrary Lagrangian-Eulerian discontinuous Galerkin (ALE-DG) method for solving one-dimensional hyperbolic equations involving delta-singularities on moving meshes. The L-2 and negative norm error estimates are proven for the ALE-DG approximation. More precisely, when choosing the approximation space with piecewise kth degree polynomials, the convergence rate in L-2-norm for the scheme with the upwind numerical flux is (k + 1)th order in the region apart from the singularities, the convergence rate in H-(k+1) norm for the scheme with the monotone fluxes in the whole domain is kth order, the convergence rate in H-(k+2) norm for the scheme with the upwind flux in the whole domain can achieve (k+ 1/2)th order, and the convergence rate in H-(k+1) (RR-T) norm for the scheme with the upwind flux is (2k +1)th order, where R-T is the pollution region at time T due to the singularities. Moreover, numerically the (2k + 1)th order accuracy for the postprocessed solution in the smooth region can be obtained, which is produced by convolving the ALE-DG solution with a suitable kernel consisting of B-splines. Numerical examples are shown to demonstrate the accuracy and capability of the ALE-DG method for the hyperbolic equations involving delta-singularity on moving meshes.
机译:在本文中,我们开发和分析了一种任意拉格朗日 - 欧拉不连续的Galerkin(ALE-DG)方法,用于求解涉及移动网格上的三维双曲线方程。为ALE-DG近似证明L-2和负值误差估计值。更确切地说,在选择具有分段kth度多项式的近似空间时,对于具有Unumlind数值的方案的L-2-NURM的收敛速率是(k + 1)除了奇点,收敛速度在H-(k + 1)规范中,具有整个领域的单调通量的方案是kth阶,H-(k + 2)标准的收敛速率对于整个领域的UPWIND通量的方案可以实现( K + 1/2)TH顺序,以及具有Upwind通量的方案的H-(k + 1)(R RT)标准的收敛速率为(2k +1),其中Rt是污染区域由于奇点。此外,可以获得平滑区域中的后处理溶液的数值(2k + 1)顺序精度,这是通过将ALE-DG溶液与由B样条组成的合适的核旋转而产生的。示出了数值示例,以证明ALE-DG方法对于涉及移动网格上的δ奇异性的双曲线方程的ALE-DG方法的准确性和能力。

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