In this paper a duality-based a posteriori error analysis is developed for the conforming hp Galerkin finite element approximation of second-order elliptic problems. Duality arguments combined with Galerkin orthogonalty yield representations of the error in arbitrary quantities of interest. From these error estimates, criteria are derived for the simultaneous adaptation of the mesh size h and t...

We investigate a purely combinatorial approach to the following mesh reenement problem: Given a coarse mesh of polygons in three-dimensional space, nd a decomposition into well-shaped quadrilaterals such that the resulting mesh is conforming and satisses prescribed local density constraints. We present a new approach based on network ow techniques. In particular, we show that this problem can e...

This paper describes an approach to construct unstructured tetrahedral and hexahedral meshes for a domain with multiple materials. We have developed an octree-based isocontouring method to construct unstructured 3D meshes for a single material domain. Based on it, we analyze each material change edge instead of sign change edge to figure out interfaces between two materials, and mesh each mater...

We propose a family of methods for simulating two-dimensional incompressible, low Reynolds number flow around a moving obstacle whose motion is prescribed. The methods make use of a universal mesh: a fixed background mesh that adapts to the geometry of the immersed obstacle at all times by adjusting a few elements in the neighborhood of the obstacle’s boundary. The resulting mesh provides a con...

An adaptive mixed finite element method (AMFEM) is designed to guarantee an error reduction, also known as saturation property: after each refinement step, the error for the fine mesh is strictly smaller than the error for the coarse mesh up to oscillation terms. This error reduction property is established here for the Raviart–Thomas finite element method with a reduction factor ρ < 1 uniforml...

This article deals with solving partial differential equations with the finite element method on hybrid non-conforming hexahedral-tetrahedral meshes. By non-conforming, we mean that a quadrangular face of a hexahedron can be connected to two triangular faces of tetrahedra. We introduce a set of low-order continuous (C) finite element spaces defined on these meshes. They are built from standard ...

We present a family of pairs of finite element spaces for the unaltered Hellinger–Reissner variational principle using polynomial shape functions on a single triangular mesh for stress and displacement. There is a member of the family for each polynomial degree, beginning with degree two for the stress and degree one for the displacement, and each is stable and affords optimal order approximati...

We propose an algorithm to compute a conforming Delaunay mesh of a bounded domain specified by a piecewise linear complex. Arbitrarily small input angles are allowed, and the input complex is not required to be a manifold. Our algorithm encloses the input edges with a small buffer zone, a union of balls whose sizes are proportional to the local feature sizes at their centers. In the output mesh...

We are concerned with Delaunay mesh generation methods and mesh adaptivity issues Planar surface and volume meshing have been automated to a large extent Over the last few years meshing activities have been focused on adap tive schemes where the features of a solution eld must be accurately captured To this end meshing techniques must be revisited in order to be capable of complet ing high qual...