Error estimates for the space-semidiscrete approximation of solutions of the wave equation in polygons G ⊂ R are presented. Based on corner asymptotics of solutions of the wave equation, it is shown that for continuous, simplicial Lagrangian Finite Elements of polynomial degree p ≥ 1 with either suitably graded mesh refinement or with bisection tree mesh refinement towards the corners of G, the...

Simulation of wall-bounded turbulent flows poses significant challenges and requires tightly controlled mesh spacing and structure near the walls. Semi-structured or hybrid meshes are often used for turbulent boundary layer flows. These meshes not only account for complex geometry but also maintain highly anisotropic, graded and layered elements near the walls. However, for engineering flow pro...

In this paper, we examine prospects for the manufacture of patient-specific biomedical implants replacing hard tissues (bone), particularly knee and hip stems and large bone (femoral) intramedullary rods, using additive manufacturing (AM) by electron beam melting (EBM). Of particular interest is the fabrication of complex functional (biocompatible) mesh arrays. Mesh elements or unit cells can b...

We describe a complete solution for both sequential and parallel construction of guaranteed quality Delaunay meshes for general two-dimensional geometries. We generalize the existing sequential point placement strategies for guaranteed quality mesh refinement: instead of a specific position for a new point, we derive two types of two-dimensional regions which we call selection disks. Both types...

This paper presents thermal buckling analysis of rectangular functionally graded plates (FG plates) with an eccentrically located elliptic cutout. The plate governing equations derived by the first order shear deformation theory (FSDT) and finite element formulation is developed to analyze the plate behavior subjected to a uniform temperature rise across plate thickness. It is assumed that the ...

We propose a projection-based implicit modeling method (PIMM) for functionally graded lattice optimization, which does not require any homogenization techniques. In this method, parametric projection function is proposed to link the of with finite element background mesh. To reduce number design variables, radial basis utilized interpolate field. The triply periodic minimal surface employed dem...

This paper is concerned with a specific finite element strategy for solving elliptic boundary value problems in domains with corners and edges. First, the anisotropic singular behaviour of the solution is described. Then the finite element method with anisotropic, graded meshes and piecewise linear shape functions is investigated for such problems; the schemes exhibit optimal convergence rates ...

Superconvergence in the L2-norm for the Galerkin approximation of the integral equation Lu = f is studied, where I is a strongly elliptic pseudodifferential operator on a smooth, closed or open curve. Let Uf, be the Galerkin approximation to u . By using the ^-operator, an operator that averages the values of uh , we will construct a better approximation than uh itself. That better approximatio...