An Ultra-weak Discontinuous Galerkin Method for Schrödinger Equation in One Dimension
نویسندگان
چکیده
منابع مشابه
A New Multiscale Discontinuous Galerkin Method for the One-Dimensional Stationary Schrödinger Equation
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...
متن کاملSuperconvergence of Discontinuous Galerkin Method for Linear Hyperbolic Equations in One Space Dimension∗
In this paper, we study the superconvergence of the error between the discontinuous Galerkin (DG) finite element solution and the exact solution for linear conservation laws when upwind fluxes are used. We prove that if we apply piecewise k-th degree polynomials, the error between the DG solution and the exact solution is (k+2)-th order superconvergent at the downwind-biased Radau points with s...
متن کاملArbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws: Analysis and application in one dimension
In this paper, we develop and analyze an arbitrary Lagrangian-Eulerian discontinuous Galerkin (ALE-DG) method with a time-dependent approximation space for one dimensional conservation laws, which satisfies the geometric conservation law. For the semi-discrete ALE-DG method, when applied to nonlinear scalar conservation laws, a cell entropy inequality, L2 stability and error estimates are prove...
متن کاملSuperconvergence of Discontinuous Galerkin Method for Scalar Nonlinear Conservation Laws in One Space Dimension
Abstract. In this paper, the analysis of the superconvergence property of the discontinuous Galerkin (DG) method applied to one-dimensional time-dependent nonlinear scalar conservation laws is carried out. We prove that the error between the DG solution and a particular projection of the exact solution achieves (k+ 3 2 )-th order superconvergence when upwind fluxes are used. The results hold tr...
متن کاملA Galerkin Radial Basis Function Method for the Schrödinger Equation
In this article, we consider the discretization of the time-dependent Schrödinger equation using radial basis functions (RBFs). We formulate the discretized problem over an unbounded domain without imposing explicit boundary conditions. Since we can show that time stability of the discretization is not guaranteed for an RBF-collocation method, we propose to employ a Galerkin ansatz instead. For...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Scientific Computing
سال: 2018
ISSN: 0885-7474,1573-7691
DOI: 10.1007/s10915-018-0789-4