A variational multiscale interpolating element-free Galerkin method for convection-diffusion and Stokes problems

Zhang, Tao; Li, Xin

doi:10.1016/j.enganabound.2017.06.013

Cited by 29 publications

(4 citation statements)

References 36 publications

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“…Then following references [62][63][64], the trial and weight functions of the fine-scale are given by…”

Section: The Iimls Methodsmentioning

confidence: 99%

“…Following reference [63], the value of coarse scale can be seen as a constant for the value of fine scale on E cell k . Then substituting Eqs.…”

Section: The Iimls Methodsmentioning

confidence: 99%

“…Using the collocation method of high-order polynomial approximation, Ömer studied the numerical solution of 3D CD problems with high Reynolds [62]. Zhang et al [63] presented a VMIEFG method for the singularly perturbed two-dimensional CD problems.…”

Section: Introductionmentioning

confidence: 99%

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A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

Wang¹,

Wu²,

Xu³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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By introducing the dimensional splitting (DS) method into the multiscale interpolating element-free Galerkin (VMIEFG) method, a dimension-splitting multiscale interpolating element-free Galerkin (DS-VMIEFG) method is proposed for three-dimensional (3D) singular perturbed convection-diffusion (SPCD) problems. In the DS-VMIEFG method, the 3D problem is decomposed into a series of 2D problems by the DS method, and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method. The improved interpolation-type moving least squares (IIMLS) method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems. The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems. The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes. For extremely small singular diffusion coefficients, the numerical solution will avoid numerical oscillation and has high computational stability. KEYWORDSDimension-splitting multiscale interpolating element-free Galerkin (DS-VMIEFG) method; interpolating variational multiscale element-free Galerkin (VMIEFG) method; dimension splitting method; singularly perturbed convection-diffusion problems

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“…Then following references [62][63][64], the trial and weight functions of the fine-scale are given by…”

Section: The Iimls Methodsmentioning

confidence: 99%

“…Following reference [63], the value of coarse scale can be seen as a constant for the value of fine scale on E cell k . Then substituting Eqs.…”

Section: The Iimls Methodsmentioning

confidence: 99%

See 1 more Smart Citation

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

Wang¹,

Wu²,

Xu³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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show abstract

“…Example 1. The first example is a convection-diffusion problem with the following exact solution [56]:…”

Section: Endmentioning

confidence: 99%

A Dimension Splitting Generalized Interpolating Element-Free Galerkin Method for the Singularly Perturbed Steady Convection–Diffusion–Reaction Problems

et al. 2021

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By introducing the dimension splitting method (DSM) into the generalized element-free Galerkin (GEFG) method, a dimension splitting generalized interpolating element-free Galerkin (DS-GIEFG) method is presented for analyzing the numerical solutions of the singularly perturbed steady convection–diffusion–reaction (CDR) problems. In the DS-GIEFG method, the DSM is used to divide the two-dimensional CDR problem into a series of lower-dimensional problems. The GEFG and the improved interpolated moving least squares (IIMLS) methods are used to obtain the discrete equations on the subdivision plane. Finally, the IIMLS method is applied to assemble the discrete equations of the entire problem. Some examples are solved to verify the effectiveness of the DS-GIEFG method. The numerical results show that the numerical solution converges to the analytical solution with the decrease in node spacing, and the DS-GIEFG method has high computational efficiency and accuracy.

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Analysis and application of the interpolating element-free Galerkin method for extended Fisher–Kolmogorov equation which arises in brain tumor dynamics modeling

Ilati

2019

Numer Algor

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A variational multiscale interpolating element-free Galerkin method for convection-diffusion and Stokes problems

Cited by 29 publications

References 36 publications

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

A Dimension Splitting Generalized Interpolating Element-Free Galerkin Method for the Singularly Perturbed Steady Convection–Diffusion–Reaction Problems

Analysis and application of the interpolating element-free Galerkin method for extended Fisher–Kolmogorov equation which arises in brain tumor dynamics modeling

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