Split-hom together structure is a new heavy load rack structure, and its reliability needs to be verified. Through analyzing multimodal hom-connection principle from the perspective of bionics and contact mechanics, the article puts forward three kinds of hom-connection methods and establishes the finite element model and mathematical model of the rack. Afterwards, the finite element model and ...

For a model Helmholtz problem at high wavenumber we present a wavenumber-explicit error analysis in weak norms such as L, H. In 1D, we analyze the convergence behavior of the lowest order optimally blended spectral-finite element scheme of [Ainsworth & Wajid, SIAM J. Numer. Anal. (2010)].

The performance of multigrid methods for the standard Poisson problem and for the consistent Poisson problem arising in spectral element discretizations of the Navier-Stokes equations is investigated. It is demonstrated that overlapping additive Schwarz methods are effective smoothers, provided that the solution in the overlap region is weighted by the inverse counting matrix. It is also shown ...

This paper describes an automated procedure to model imprecisely defined structures and solve them using the interval and fuzzy finite element methods (IFEM and FFEM). The IFEM and FFEM procedures both require an uncertain FE model as input. Since none of the available preprocessors can generate uncertain FE models, the first part of the research focuses on creating an uncertain FE model based ...

In hot forming process, the workpiece undergoes plastic deformation at high temperature and the microstructure of the workpiece changes according to the plastic deformation. These changes affect the mechanical properties of workpiece. In order to optimize this process, both the plastic deformation of workpiece and its microstructural changes should be taken into consideration. Since material be...

Abstract. We consider the first family of H(curl,Ω)-conforming Nedéléc finite elements on tetrahedral meshes. Spectral approximation (p-version) is achieved by keeping the mesh fixed and raising the polynomial degree p uniformly in all mesh cells. We prove that the associated subspaces of discretely weakly divergence free piecewise polynomial vector fields enjoy a long conjectured discrete comp...

An orthogonal system of rational functions is introduced. Some results on rational approximations based on various orthogonal projections and interpolations are established. These results form the mathematical foundation of the related spectral method and pseudospectral method for solving differential equations on the half line. The error estimates of the rational spectral method and rational p...

We present a numerical method, based on a coupling of finite elements and boundary elements, to solve a fluid–solid interaction problem posed in the plane. The boundary unknowns involved in our formulation are approximated by a spectral method. We provide error estimates for the Galerkin method and present numerical results that illustrate the accuracy of our scheme.

Polynomial extensions play a vital role in the analysis of the p and h-p FEM and the spectral element method. We construct explicitly polynomial extensions on standard elements: cubes, triangular prisms and pyramids, which together with the extension on tetrahedrons are used by the p and h-p FEM in three dimensions. These extensions are proved to be stable and compatible with FEM subspaces on t...

Polynomial extensions play a vital role in analysis of the p and h-p FEM as well as spectral element method. In this paper, we construct explicitly polynomial extensions on a triangle T and a square S, which lift a polynomial defined on a side Γ or on whole boundary of T or S. The continuity of these extension operators from H 1 2 00(Γ) to H (T ) or H(S) and from H 1 2 (∂T ) to H(T ) or from H ...