A New Multiscale Discontinuous Galerkin Method for the One-Dimensional Stationary Schrödinger Equation
A New Multiscale Discontinuous Galerkin Method for the One-Dimensional Stationary Schrödinger Equation
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DOI：
10.1007/s10915-015-0022-7
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发表时间：
2015-04
影响因子：
2.5
通讯作者：
B. Dong;Chi-Wang Shu;Wei Wang
中科院分区：
文献类型：
--
作者：
B. Dong;Chi-Wang Shu;Wei Wang
In this paper, we develop and analyze a new multiscale discontinuous Galerkin (DG) method for one-dimensional stationary Schrödinger equations with open boundary conditions which have highly oscillating solutions. Our method uses a smaller finite element space than the WKB local DG method proposed in Wang and Shu (J Comput Phys 218:295–323, 2006) while achieving the same order of accuracy with no resonance errors. We prove that the DG approximation converges optimally with respect to the mesh sizeinnorm without the typical constraint thathas to be smaller than the wave length. Numerical experiments were carried out to verify the second order optimal convergence rate of the method and to demonstrate its ability to capture oscillating solutions on coarse meshes in the applications to Schrödinger equations.
