Interior penalty discontinuous Galerkin technique for solving generalized Sobolev equation
DOI10.1016/j.apnum.2020.03.019zbMath1437.65174OpenAlexW3013924237MaRDI QIDQ2174967
Mehdi Dehghan, Mostafa Abbaszadeh
Publication date: 27 April 2020
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.apnum.2020.03.019
stabilitydiscontinuous Galerkin methoderror estimateSobolev equationconvergence orderCrank-Nicolson idea
Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55)
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- Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media
- A class of discontinuous Petrov-Galerkin methods. III: Adaptivity
- Weak Galerkin finite element methods for Sobolev equation
- Numerical investigation of homogenized Stokes-Nernst-Planck-Poisson systems
- On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes
- High-order local discontinuous Galerkin method combined with WSGD-approximation for a fractional subdiffusion equation
- \(hp\)-adaptive composite discontinuous Galerkin methods for elliptic eigenvalue problems on complicated domains
- A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
- The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
- Analysis of two methods based on Galerkin weak form for fractional diffusion-wave: meshless interpolating element free Galerkin (IEFG) and finite element methods
- Local discontinuous Galerkin method for a nonlinear time-fractional fourth-order partial differential equation
- A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations
- A sequential discontinuous Galerkin method for the coupling of flow and geomechanics
- An expanded mixed finite element method for two-dimensional Sobolev equations
- On discrete maximum principles for discontinuous Galerkin methods
- Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I
- A POD-based reduced-order Crank-Nicolson finite volume element extrapolating algorithm for 2D Sobolev equations
- A mass-conservative characteristic splitting mixed finite element method for convection-dominated Sobolev equation
- FESTUNG: A~MATLAB/GNU~Octave~toolbox for the discontinuous Galerkin method. I: Diffusion operator
- Error analysis of primal discontinuous Galerkin methods for a mixed formulation of the Biot equations
- Analysis of mixed finite element method (MFEM) for solving the generalized fractional reaction-diffusion equation on nonrectangular domains
- Nonconforming virtual element method for the time fractional reaction-subdiffusion equation with non-smooth data
- Investigation of the Oldroyd model as a generalized incompressible Navier-Stokes equation via the interpolating stabilized element free Galerkin technique
- Unconditional superconvergence analysis of the conservative linearized Galerkin FEMs for nonlinear Klein-Gordon-Schrödinger equation
- The well-posedness of solution to semilinear pseudo-parabolic equation
- A reduced-order extrapolated finite difference iterative scheme based on POD method for 2D Sobolev equation
- A multilevel Monte Carlo finite element method for the stochastic Cahn-Hilliard-Cook equation
- A fast energy conserving finite element method for the nonlinear fractional Schrödinger equation with wave operator
- Estimation of penalty parameters for symmetric interior penalty Galerkin methods
- Explicit and implicit solutions for the one-dimensional cubic and quintic complex Ginzburg-Landau equations
- Variational multiscale element free Galerkin (VMEFG) and local discontinuous Galerkin (LDG) methods for solving two-dimensional Brusselator reaction-diffusion system with and without cross-diffusion
- Efficient time discretization for local discontinuous Galerkin methods
- Locally conservative discontinuous Petrov-Galerkin finite elements for fluid problems
- Galerkin methods for nonlinear Sobolev equations
- Stability and Error Estimates of Local Discontinuous Galerkin Methods with Implicit-Explicit Time-Marching for Advection-Diffusion Problems
- Application of semi‐analytical methods for solving the Rosenau‐Hyman equation arising in the pattern formation in liquid drops
- Analysis of a local discontinuous Galerkin method for time‐fractional advection‐diffusion equations
- The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
- Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
- TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
- Numerical Solution of Sobolev Partial Differential Equations
- The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
- A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations
- An efficient difference scheme for the coupled nonlinear fractional Ginzburg–Landau equations with the fractional Laplacian
- Discontinuous Galerkin method for solving the black‐oil problem in porous media
- Galerkin finite element method for higher dimensional multi-term fractional diffusion equation on non-uniform meshes
- Fourth Order Exponential Time Differencing Method with Local Discontinuous Galerkin Approximation for Coupled Nonlinear Schrödinger Equations
- Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent Developments
- Devising discontinuous Galerkin methods for nonlinear hyperbolic conservation laws