Jufeng Wang¹, Yong Wu¹, Ying Xu¹, Fengxin Sun^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 341-356, 2023, DOI:10.32604/cmes.2022.023140

Abstract 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… More >

Pratibhamoy Das¹, Srinivasan Natesan²

CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.6, pp. 463-485, 2013, DOI:10.3970/cmes.2013.090.463

Abstract Adaptive mesh generation has become a valuable tool for the improvements of accuracy and efficiency of numerical solutions over fixed number of meshes. This paper gives an interpretation of the concept of equidistribution for singularly perturbed problems to obtain higher-order accuracy. We have used the post-processing Richardson extrapolation technique to improve the accuracy of the parameter uniform computed solution, obtained on a mesh which is adaptively generated by equidistributing a monitor function. Numerical examples demonstrate the high quality behavior of the computed solution. More >