An Ultra-weak Discontinuous Galerkin Method for Schrödinger Equation in One Dimension

Anqi Chen; Fengyan Li; Yingda Cheng

doi:10.1007/s10915-018-0789-4

An Ultra-weak Discontinuous Galerkin Method for Schrödinger Equation in One Dimension

Journal of Scientific Computing ◽

10.1007/s10915-018-0789-4 ◽

2018 ◽

Vol 78 (2) ◽

pp. 772-815 ◽

Cited By ~ 2

Author(s):

Anqi Chen ◽

Fengyan Li ◽

Yingda Cheng

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

One Dimension

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Mean-square convergence of a symplectic local discontinuous Galerkin method applied to stochastic linear Schrödinger equation

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drw023 ◽

2016 ◽

pp. drw023

Author(s):

Chuchu Chen ◽

Jialin Hong ◽

Lihai Ji

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Mean Square ◽

Local Discontinuous Galerkin ◽

Mean Square Convergence

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A New Multiscale Discontinuous Galerkin Method for the One-Dimensional Stationary Schrödinger Equation

Journal of Scientific Computing ◽

10.1007/s10915-015-0022-7 ◽

2015 ◽

Vol 66 (1) ◽

pp. 321-345 ◽

Cited By ~ 5

Author(s):

Bo Dong ◽

Chi-Wang Shu ◽

Wei Wang

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Stationary Schrödinger Equation ◽

One Dimensional ◽

The One

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A conservative local discontinuous Galerkin method for the solution of nonlinear Schrödinger equation in two dimensions

Science China Mathematics ◽

10.1007/s11425-016-9118-x ◽

2017 ◽

Vol 60 (12) ◽

pp. 2515-2530 ◽

Cited By ~ 6

Author(s):

RongPei Zhang ◽

XiJun Yu ◽

MingJun Li ◽

XiangGui Li

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Nonlinear Schrödinger Equation ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Nonlinear Schrodinger Equation ◽

Two Dimensions ◽

Local Discontinuous Galerkin

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The WKB Local Discontinuous Galerkin Method for the Simulation of Schrödinger Equation in a Resonant Tunneling Diode

Journal of Scientific Computing ◽

10.1007/s10915-008-9237-1 ◽

2008 ◽

Vol 40 (1-3) ◽

pp. 360-374 ◽

Cited By ~ 14

Author(s):

Wei Wang ◽

Chi-Wang Shu

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Resonant Tunneling ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Resonant Tunneling Diode ◽

Local Discontinuous Galerkin ◽

Tunneling Diode

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Analysis of an implicit fully discrete local discontinuous Galerkin method for the time-fractional Schrödinger equation

Finite Elements in Analysis and Design ◽

10.1016/j.finel.2012.03.008 ◽

2012 ◽

Vol 59 ◽

pp. 28-34 ◽

Cited By ~ 62

Author(s):

Leilei Wei ◽

Yinnian He ◽

Xindong Zhang ◽

Shaoli Wang

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Fractional Schrödinger Equation ◽

Fully Discrete ◽

Local Discontinuous Galerkin ◽

Fractional Schrodinger Equation

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A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method

Mathematics of Computation ◽

10.1090/s0025-5718-98-00946-6 ◽

1998 ◽

Vol 67 (222) ◽

pp. 479-500 ◽

Cited By ~ 80

Author(s):

Ohannes Karakashian ◽

Charalambos Makridakis

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Space Time ◽

Nonlinear Schrodinger Equation ◽

Element Method

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Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws: Analysis and application in one dimension

Mathematics of Computation ◽

10.1090/mcom/3126 ◽

2016 ◽

Vol 86 (305) ◽

pp. 1203-1232 ◽

Cited By ~ 10

Author(s):

Christian Klingenberg ◽

Gero Schnücke ◽

Yinhua Xia

Keyword(s):

Conservation Laws ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

One Dimension ◽

Arbitrary Lagrangian Eulerian

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Error estimates for the third order explicit Runge-Kutta discontinuous Galerkin method for a linear hyperbolic equation in one-dimension with discontinuous initial data

Numerische Mathematik ◽

10.1007/s00211-013-0573-1 ◽

2013 ◽

Vol 126 (4) ◽

pp. 703-740 ◽

Cited By ~ 21

Author(s):

Qiang Zhang ◽

Chi-Wang Shu

Keyword(s):

Initial Data ◽

Galerkin Method ◽

Hyperbolic Equation ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

One Dimension ◽

Third Order ◽

Linear Hyperbolic Equation ◽

The Third ◽

Discontinuous Initial Data

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Optimal error estimate of conservative local discontinuous Galerkin method for nonlinear Schrödinger equation

Applied Numerical Mathematics ◽

10.1016/j.apnum.2018.01.004 ◽

2018 ◽

Vol 127 ◽

pp. 164-178 ◽

Cited By ~ 10

Author(s):

Jialin Hong ◽

Lihai Ji ◽

Zhihui Liu

Keyword(s):

Error Estimate ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Nonlinear Schrodinger Equation ◽

Optimal Error Estimate ◽

Optimal Error ◽

Local Discontinuous Galerkin

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Superconvergence of Ultra-Weak Discontinuous Galerkin Methods for the Linear Schrödinger Equation in One Dimension

Journal of Scientific Computing ◽

10.1007/s10915-020-01124-0 ◽

2020 ◽

Vol 82 (1) ◽

Author(s):

Anqi Chen ◽

Yingda Cheng ◽

Yong Liu ◽

Mengping Zhang

Keyword(s):

Schrödinger Equation ◽

Discontinuous Galerkin ◽

Schrodinger Equation ◽

Discontinuous Galerkin Methods ◽

One Dimension ◽

Galerkin Methods

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