In tetrahedral mesh generation, the constraints imposed by adaptive element size, good tetrahedral quality (shape measured by some local metric), and material boundaries are often in conflict. Attempts to satisfy these conditions simultaneously frustrate many conventional approaches. We propose a new strategy for boundary conforming meshing that decouples the problem of building tetrahedra of p...

We propose a 3D conforming-nonconforming mixed finite element for solving symmetric stress Stokes equations. The low-order conforming finite elements are not inf-sup stable. The low-order nonconforming finite elements do not satisfy the Korn inequality. The proposed finite element space consists of two conforming components and one nonconforming component. We prove that the discrete inf-sup con...

This paper describes a new method for increasing the number and the volume of hexahedral and prism elements in a hexdominant mesh by topological transformations. The method takes as input a hex-dominant mesh consisting of hexahedrons, prisms, pyramids and tetrahedrons and modifies the mesh to increase the number and the volume of hexahedrons and prisms while maintaining the relaxed conformity c...

First we introduce a mesh density function that serves as a criterion to decide, where a simplicial mesh should be fine (dense) and where it should be coarse. Further, we propose a new bisection algorithm that chooses for bisection an edge in a given mesh associated with the maximum value of the mesh density function. Dividing this edge at its midpoint, we correspondingly bisect all simplices s...

We present a new algorithm for the generation of hexahedral element meshes. The algorithm starts with an octree discretization of the interior of the input object which is converted to a conforming hexahedral element mesh. Then the isomorphism technique 9] is used to adapt the mesh to the object boundary.

We consider a conforming finite element approximation of the Reissner-Mindlin system. We propose a new robust a posteriori error estimator based on H(div ) conforming finite elements and equilibrated fluxes. It is shown that this estimator gives rise to an upper bound where the constant is one up to higher order terms. Lower bounds can also be established with constants depending on the shape r...

Hierarchical Powell-Sabin splines are C-continuous piecewise quadratic polynomials defined on a hierarchical triangulation. The mesh is obtained by partitioning an initial conforming triangulation locally with a triadic split, so that it is no longer conforming. We propose a normalized quasi-hierarchical basis for this spline space. The B-spline basis functions have a local support, they form a...

In this study, a new adhesive contact model is built upon boundary element method (BEM) developed by Pohrt and Popov (2015). The strain energy release rate (SERR) on the edge of bonding interface evaluated using Virtual Crack Closure Technique (VCCT) which shown to have better accuracy weaker mesh-size dependency than closed-form SERR formula derived Popov. A composite delamination criterion pr...

A flow solver based on a mixed mesh paradigm is developed for resolving flows in a high-order accurate manner. The proposed mesh topology involves unstructured tetrahedral/prismatic mesh in the near-body region and adaptive Cartesian-based unstructured mesh in the off-body region. The body-conforming near-body unstructured mesh offers a great flexibility in treating complex geometries, and also...