Given a complex of vertices, constraining segments (and planar straight-line constraining facets in 3D) and an-Lipschitz control spacing function f() over the domain, an algorithm presented herein can generate a conforming mesh of Delaunay triangles (tetrahedra in 3D) whose circumradius-to-shortest-edge ratios are no greater than p 2 (2 in 3D). The triangle (tetra-hedron) size is within a const...

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...

A mesh insertion method is presented to merge a tool mesh into a target mesh. All the entities of the tool mesh are preserved in the output mesh while some of the entities of the target mesh are modified or eliminated in order to obtain a topologically conforming mesh. The algorithm can handle non-manifold surfaces formed of quadrilaterals and/or triangles as well as volumetric meshes based on ...

Nowadays, numerical modelings play a key role in analyzing hydraulic problems in fractured rock media. The discrete fracture network model is one of the most used numerical models to simulate the geometrical structure of a rock-mass. In such media, discontinuities are considered as discrete paths for fluid flow through the rock-mass while its matrix is assumed impermeable. There are two main pa...

We prove the stability in H(Ω) of the L projection onto a family of finite element spaces of conforming piecewise linear functions satisfying certain local mesh conditions. We give explicit formulae to check these conditions for a given finite element mesh in any number of spatial dimensions. In particular, stability of the L projection in H(Ω) holds for locally quasiuniform geometrically refin...

Mesh adaptation methods can improve the efficiency and accuracy of solutions to computational modeling problems. In many applications involving quadrilateral and hexahedral meshes, local modifications which maintain the original element type are desired. For triangle and tetrahedral meshes, effective refinement and coarsening methods that satisfy these criteria are available. Refinement methods...

We address fundamental aspects in the approximation theory of vector-valued finite element methods, using exterior calculus as a unifying framework. generalize Clément interpolant and Scott-Zhang to differential forms, we derive broken Bramble-Hilbert lemma. Our interpolants require only minimal smoothness assumptions respect partial boundary conditions. This permits us state local error estima...

In this paper we present a local refinement algorithm based on the longest-edge trisection of triangles. Local trisection patterns are sed to generate a conforming triangulation, depending on the number of non-conforming nodes per edge presented. We describe he algorithm and provide a study of the efficiency (cost analysis) of the triangulation refinement problem. The algorithm presented, nd it...

This paper reviews the main features of a high-order nondissipative discontinuous Galerkin (DG) method recently investigated in [1]-[3] for solving Maxwell’s equations on non-conforming simplex meshes. The proposed method combines a centered approximation for the numerical fluxes at inter element boundaries, with either a secondorder or a fourth-order leap-frog time integration scheme. Moreover...

The Delaunay Refinement Algorithm for quality meshing is extended to three dimensions. The algorithm accepts input with arbitrarily small angles, and outputs a Conforming Delaunay Tetrahedralization where most tetrahedra have radius-to-shortest-edge ratio smaller than some user chosen μ > 2. Those tets with poor quality are in well defined locations: their circumcenters are describably near inp...