Error analysis and numerical simulation of magnetohydrodynamics (MHD) equation based on the interpolating element free Galerkin (IEFG) method

DOI10.1016/j.apnum.2018.10.004zbMath1412.65070OpenAlexW2896533445WikidataQ129054163 ScholiaQ129054163MaRDI QIDQ1728346

Mehdi Dehghan, Mostafa Abbaszadeh

Publication date: 22 February 2019

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2018.10.004

zbMATH Keywords

convergenceunconditional stabilityelement free Galerkin (EFG) methodinterpolating element free Galerkin techniqueinterpolating moving least squares approximationmagnetohydrodynamics (MHD) equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) 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) Magnetohydrodynamics and electrohydrodynamics (76W05) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical quadrature and cubature formulas (65D32)

Related Items (32)

A new analysis of Galerkin Legendre spectral methods for coupled hyperbolic/parabolic system arising in unsteady MHD flow of Maxwell fluid and numerical simulation ⋮ Numerical investigation of the magnetic properties and behavior of electrically conducting fluids via the local weak form method ⋮ A local scheme for numerical simulation of multi-dimensional dynamic quantum model: application to decision-making ⋮ A reduced order modeling method based on GNAT-embedded hybrid snapshot simulation ⋮ Convergence analysis and error estimates of the interpolating element-free Galerkin method for the evolutionary variational inequality of the second-order in time ⋮ A simple staggered approach for comprehensive analysis of forced convection heat transfer using the improved element-free Galerkin-reduced integration penalty method to solve the fluid dynamics problem ⋮ A three level linearized compact difference scheme for a fourth-order reaction-diffusion equation ⋮ Application of direct meshless local <scp>Petrov–Galerkin</scp> method for numerical solution of stochastic elliptic interface problems ⋮ The interpolating element-free Galerkin method for three-dimensional elastoplasticity problems ⋮ A new error estimation technique for solving torsion bar problem with inclusion by using BEM ⋮ Element-free Galerkin analysis of Stokes problems using the reproducing kernel gradient smoothing integration ⋮ Comparison study on the numerical stability of dual reciprocity boundary element method for the MHD slip flow problem ⋮ The interpolating element-free Galerkin method for the \(p\)-Laplace double obstacle mixed complementarity problem ⋮ A Nitsche-Based Element-Free Galerkin Method for Semilinear Elliptic Problems ⋮ An element-free Galerkin method for the obstacle problem ⋮ A divergence-free generalized moving least squares approximation with its application ⋮ Numerical analysis of fully discrete energy stable weak Galerkin finite element scheme for a coupled Cahn-Hilliard-Navier-Stokes phase-field model ⋮ Phase distribution control of neural oscillator populations using local radial basis function meshfree technique with application in epileptic seizures: a numerical simulation approach ⋮ A hybrid generalized interpolated element-free Galerkin method for Stokes problems ⋮ Analysis and application of the interpolating element free Galerkin (IEFG) method to simulate the prevention of groundwater contamination with application in fluid flow ⋮ Investigation of the Oldroyd model as a generalized incompressible Navier-Stokes equation via the interpolating stabilized element free Galerkin technique ⋮ A fourth-order numerical scheme for singularly perturbed delay parabolic problem arising in population dynamics ⋮ On the static analysis of inhomogeneous magneto-electro-elastic plates in thermal environment via element-free Galerkin method ⋮ Numerical study of the unsteady 2D coupled magneto-hydrodynamic equations on regular/irregular pipe using direct meshless local Petrov-Galerkin method ⋮ Exact and FDM solutions of 1D MHD flow between parallel electrically conducting and slipping plates ⋮ DRBEM solution of MHD flow in a rectangular duct with time-varied external magnetic field ⋮ A leap-frog meshless method with radial basis functions for simulating electromagnetic wave splitter and rotator ⋮ The element-free Galerkin method for the variational-hemivariational inequality of the dynamic Signorini-Tresca contact problems with friction in elastic materials ⋮ The high-order smooth interpolated reproducing kernel particle method for elastodynamics problems ⋮ A complex variable EFG method for hyperelastic large deformation analysis under non-conservative loads ⋮ Stabilized FEM solution of MHD duct flow with conducting cracks in the insulation ⋮ Stabilizing subgrid FEM solution of the natural convection flow under high magnitude magnetic field on sinusoidal corrugated enclosure

Cites Work

• The boundary elements method for magneto-hydrodynamic (MHD) channel flows at high Hartmann numbers
• The Galerkin boundary node method for magneto-hydrodynamic (MHD) equation
• Upwinding meshfree point collocation method for steady MHD flow with arbitrary orientation of applied magnetic field at high Hartmann numbers
• An exponential compact difference scheme for solving 2D steady magnetohydrodynamic (MHD) duct flow problems
• A numerical framework for two-dimensional large deformation of inhomogeneous swelling of gels using the improved complex variable element-free Galerkin method
• An improved element-free Galerkin method for numerical modeling of the biological population problems
• On the stability of the moving least squares approximation and the element-free Galerkin method
• An improved meshless method for solving two-dimensional distributed order time-fractional diffusion-wave equation with error estimate
• Two new upwind difference schemes for a coupled system of convection-diffusion equations arising from the steady MHD duct flow problems
• A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations
• Local radial point interpolation method for the fully developed magnetohydrodynamic flow
• Linear feedback control and approximation for a system governed by unsteady MHD equations
• A novel complex variable element-free Galerkin method for two-dimensional large deformation problems
• An accurate, stable and efficient domain-type meshless method for the solution of MHD flow problems
• The variational multiscale element free Galerkin method for MHD flows at high Hartmann numbers
• On the finite volume element method
• Fundamental solution for coupled magnetohydrodynamic flow equations
• Error estimates for the interpolating moving least-squares method in \(n\)-dimensional space
• Boundary element method solution of magnetohydrodynamic flow in a rectangular duct with conducting walls parallel to applied magnetic field
• Solution of magnetohydrodynamic flow problems using the boundary element method
• The boundary element solution of the magnetohydrodynamic flow in an infinite region
• Meshless local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity
• Functional analysis, Sobolev spaces and partial differential equations
• Magnetohydrodynamic axial flow in a triangular pipe under transverse magnetic field
• A new algorithm for solution of equations of MHD channel flows at moderate Hartmann numbers
• A novel interpolating element-free Galerkin (IEFG) method for two-dimensional elastoplasticity
• A meshless interpolating Galerkin boundary node method for Stokes flows
• Analysis of the inherent instability of the interpolating moving least squares method when using improper polynomial bases
• A reduced proper orthogonal decomposition (POD) element free Galerkin (POD-EFG) method to simulate two-dimensional solute transport problems and error estimate
• The interpolating element-free Galerkin method for 2D transient heat conduction problems
• The element-free Galerkin method for the nonlinear \(p\)-Laplacian equation
• A generalized element-free Galerkin method for Stokes problem
• Steady heat conduction analyses using an interpolating element-free Galerkin scaled boundary method
• Numerical solution of 2D Navier-Stokes equation discretized via boundary elements method and finite difference approximation
• A finite volume method based on the Crouzeix-Raviart element for elliptic PDE's in two dimensions
• The method of variably scaled radial kernels for solving two-dimensional magnetohydrodynamic (MHD) equations using two discretizations: the Crank-Nicolson scheme and the method of lines (MOL)
• Decoupled schemes for unsteady MHD equations. II: Finite element spatial discretization and numerical implementation
• Numerical solution of transient heat conduction problems using improved meshless local Petrov-Galerkin method
• Analysis of the complex moving least squares approximation and the associated element-free Galerkin method
• Proper orthogonal decomposition variational multiscale element free Galerkin (POD-VMEFG) meshless method for solving incompressible Navier-Stokes equation
• The improved complex variable element-free Galerkin method for two-dimensional Schrödinger equation
• Localized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions
• A meshfree weak-strong (MWS) form method for the unsteady magnetohydrodynamic (MHD) flow in pipe with arbitrary wall conductivity
• The improved element-free Galerkin method for two-dimensional elastodynamics problems
• The finite element method for MHD flow at high Hartmann numbers
• The interpolating element-free Galerkin (IEFG) method for two-dimensional potential problems
• An element-free IMLS-Ritz method for numerical solution of three-dimensional wave equations
• Duct flow with a transverse magnetic field at high Hartmann numbers
• The Finite Volume Element Method for Diffusion Equations on General Triangulations
• Finite difference and finite element methods for mhd channel flows
• Magnetohydrodynamic flow in electrodynamically coupled rectangular ducts
• Finite element method for solving mhd flow in a rectangular duct
• Finite element method in magnetohydrodynamic channel flow problems
• Boundary element method solution of MHD flow in a rectangular duct
• A stable boundary elements method for magnetohydrodynamic channel flows at high Hartmann numbers
• Unconditional convergence of the Euler semi-implicit scheme for the three-dimensional incompressible MHD equations
• Boundary element solution of unsteady magnetohydrodynamic duct flow with differential quadrature time integration scheme
• A finite element method for magnetohydrodynamics
• Unnamed Item

This page was built for publication: Error analysis and numerical simulation of magnetohydrodynamics (MHD) equation based on the interpolating element free Galerkin (IEFG) method