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

Anqi Chen; Yingda Cheng; Yong Liu; Mengping Zhang

doi:10.1007/s10915-020-01124-0

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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Discontinuous Galerkin methods for the linear Schrödinger equation in non-cylindrical domains

Numerische Mathematik ◽

10.1007/s00211-010-0296-5 ◽

2010 ◽

Vol 115 (4) ◽

pp. 585-608 ◽

Cited By ~ 9

Author(s):

D. C. Antonopoulou ◽

M. Plexousakis

Keyword(s):

Schrödinger Equation ◽

Discontinuous Galerkin ◽

Schrodinger Equation ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Cylindrical Domains

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High-order multiscale discontinuous Galerkin methods for the one-dimensional stationary Schrödinger equation

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.112962 ◽

2020 ◽

Vol 380 ◽

pp. 112962

Author(s):

Bo Dong ◽

Wei Wang

Keyword(s):

Schrödinger Equation ◽

Discontinuous Galerkin ◽

Schrodinger Equation ◽

Discontinuous Galerkin Methods ◽

High Order ◽

Galerkin Methods ◽

Stationary Schrödinger Equation ◽

One Dimensional ◽

The One

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Energy Conserving Local Discontinuous Galerkin Methods for the Nonlinear Schrödinger Equation with Wave Operator

Journal of Scientific Computing ◽

10.1007/s10915-014-9977-z ◽

2014 ◽

Vol 65 (2) ◽

pp. 622-647 ◽

Cited By ~ 15

Author(s):

Li Guo ◽

Yan Xu

Keyword(s):

Schrödinger Equation ◽

Discontinuous Galerkin ◽

Wave Operator ◽

Schrodinger Equation ◽

Discontinuous Galerkin Methods ◽

Nonlinear Schrodinger Equation ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Energy Conserving

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Conservative local discontinuous Galerkin methods for the cubic-quintic nonlinear Schrödinger equation

Optik ◽

10.1016/j.ijleo.2020.165821 ◽

2021 ◽

Vol 226 ◽

pp. 165821

Author(s):

He Yang

Keyword(s):

Schrödinger Equation ◽

Discontinuous Galerkin ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Discontinuous Galerkin Methods ◽

Nonlinear Schrodinger Equation ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Quintic Nonlinear Schrödinger Equation

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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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Device Modeling Using Discontinuous Galerkin Methods for Fluid Plasmas

40th AIAA Plasmadynamics and Lasers Conference ◽

10.2514/6.2009-3834 ◽

2009 ◽

Author(s):

John Loverich ◽

Ammar Hakim

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Device Modeling ◽

Galerkin Methods

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Regionally implicit discontinuous Galerkin methods for solving the relativistic Vlasov-Maxwell system

10.31274/etd-180810-5144 ◽

2017 ◽

Author(s):

Pierson Guthrey

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Maxwell System

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A Comparison of the Explicit and Implicit Hybridizable Discontinuous Galerkin Methods for Nonlinear Shallow Water Equations

Journal of Scientific Computing ◽

10.1007/s10915-019-01007-z ◽

2019 ◽

Vol 80 (3) ◽

pp. 1936-1956 ◽

Cited By ~ 3

Author(s):

Ali Samii ◽

Kazbek Kazhyken ◽

Craig Michoski ◽

Clint Dawson

Keyword(s):

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Hybridizable Discontinuous Galerkin ◽

Nonlinear Shallow Water Equations ◽

Hybridizable Discontinuous Galerkin Methods

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Abstract theory of hybridizable discontinuous Galerkin methods for second-order quasilinear elliptic problems

Computational Mathematics and Mathematical Physics ◽

10.1134/s096554251403004x ◽

2014 ◽

Vol 54 (3) ◽

pp. 474-490 ◽

Cited By ~ 5

Author(s):

R. Z. Dautov ◽

E. M. Fedotov

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Elliptic Problems ◽

Second Order ◽

Galerkin Methods ◽

Abstract Theory ◽

Hybridizable Discontinuous Galerkin ◽

Hybridizable Discontinuous Galerkin Methods ◽

Quasilinear Elliptic Problems ◽

Quasilinear Elliptic

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Local-Maximum-and-Minimum-Preserving Solution Remapping Technique to Accelerate Flow Convergence for Discontinuous Galerkin Methods in Shape Optimization Design

Journal of Scientific Computing ◽

10.1007/s10915-021-01499-8 ◽

2021 ◽

Vol 87 (3) ◽

Author(s):

Jufang Wang ◽

Tiegang Liu

Keyword(s):

Shape Optimization ◽

Discontinuous Galerkin ◽

Optimization Design ◽

Discontinuous Galerkin Methods ◽

Local Maximum ◽

Galerkin Methods ◽

Accelerate Flow ◽

Flow Convergence

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