A conservative local discontinuous Galerkin method for the solution of nonlinear Schrödinger equation in two dimensions
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Publication:681929
DOI10.1007/s11425-016-9118-xzbMath1414.65022OpenAlexW2757289526MaRDI QIDQ681929
Xiang-Gui Li, Rongpei Zhang, Ming-jun Li, Xi-Jun Yu
Publication date: 13 February 2018
Published in: Science China. Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11425-016-9118-x
nonlinear Schrödinger equationdiscontinuous Galerkin methodKrylov implicit integration factor methodmass and energy conservation
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)
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Cites Work
- Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
- A combined discontinuous Galerkin method for the dipolar Bose-Einstein condensation
- Optimal \(l^\infty\) error estimates of finite difference methods for the coupled Gross-Pitaevskii equations in high dimensions
- Krylov implicit integration factor methods for spatial discretization on high-dimensional unstructured meshes: application to discontinuous Galerkin methods
- A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients
- High-order compact ADI (HOC-ADI) method for solving unsteady 2D Schrödinger equation
- Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrödinger equations
- Compact finite difference schemes with high accuracy for one-dimensional nonlinear Schrödinger equation
- A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
- Mass preserving discontinuous Galerkin methods for Schrödinger equations
- L\({}^ 2\) concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity
- Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity
- On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
- Difference schemes for solving the generalized nonlinear Schrödinger equation
- A conservative spectral collocation method for the nonlinear Schrödinger equation in two dimensions
- Local discontinuous Galerkin methods for nonlinear Schrödinger equations
- Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
- \(B\)-spline finite element studies of the nonlinear Schrödinger equation
- Alternating direction implicit method for solving two-dimensional cubic nonlinear Schrödinger equation
- Direct discontinuous Galerkin method for nonlinear reaction-diffusion systems in pattern formation
- A Krylov semi-implicit discontinuous Galerkin method for the computation of ground and excited states in Bose-Einstein condensates
- Numerical studies on nonlinear Schrödinger equations by spectral collocation method with preconditioning
- Efficient semi-implicit schemes for stiff systems
- Analysis of the local discontinuous Galerkin method for the drift-diffusion model of semiconductor devices
- An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
- High-Order Exponential Operator Splitting Methods for Time-Dependent Schrödinger Equations
- The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
- Gaussons: Solitons of the Logarithmic Schrödinger Equation
- On Optimal Order Error Estimates for the Nonlinear Schrödinger Equation
- Vortex Ring Pinning for the Gross--Pitaevskii Equation in Three-Dimensional Space
- 二维非线性Schr\"{o}dinger方程显式格式的最大模误差分析
- Superconvergence of discontinuous Galerkin methods for time-dependent partial differential equations
- Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation
- The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems
- Fourth Order Exponential Time Differencing Method with Local Discontinuous Galerkin Approximation for Coupled Nonlinear Schrödinger Equations
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