In this paper, some current issues of Delaunay mesh generation and optimization are addressed, with particular emphasis on the robustness of the meshing procedure and the quality of the resulting mesh. We also report new progress on the robust conforming and constrained boundary recovery in three dimensions, along with the quality mesh generation based on Centroidal Voronoi tessellations. Appli...

In this paper we present dynamic adaptive meshes, a scheme for maintaining a conforming triangulation of time-varying surfaces. The user supplies an initial mesh, a surface sampling procedure and a set of adaptation criteria. The mesh is automatically modified in order to conform to user defined characteristics, while the surface changes over time. Our scheme is very simple to implement. It emp...

In this paper we develop two conforming finite element methods for a fourth order bi-wave equation arising as a simplified Ginzburg-Landau-type model for d-wave superconductors in absence of applied magnetic field. Unlike the biharmonic operator ∆2, the bi-wave operator 2 is not an elliptic operator, so the energy space for the bi-wave equation is much larger than the energy space for the bihar...

This paper proposes new finite element spaces that can be constructed for agglomerates of standard elements that have certain regular structure. The main requirement is that the agglomerates share faces that have closed boundaries composed of 1-d edges. The spaces resulting from the agglomerated elements are subspaces of the original de Rham sequence of H-conforming, H(curl) conforming, H(div) ...

Abstract. In an obstacle problems with an affine obstacle, homogeneous Dirichlet boundary conditions, and standard regularity assumptions, the Crouzeix-Raviart non-conforming finite element method (FEM) allows for linear convergence as the maximal mesh-size approaches zero. The residual-based a posteriori error analysis leads to reliable and efficient control over the error with explicit consta...

We propose a new strategy for boundary conforming meshing that decouples the problem of building tetrahedra of proper size and shape from the problem of conforming to complex, non-manifold boundaries. This approach is motivated by the observation that while several methods exist for adaptive tetrahedral meshing, they typically have difficulty at geometric boundaries. The proposed strategy avoid...

This paper extends the two-grid discretization scheme of the conforming finite elements proposed by Xu and Zhou (Math. Comput., 70 (2001), pp.17-25) to the nonconforming finite elements for eigenvalue problems. In particular, two two-grid discretization schemes based on Rayleigh quotient technique are proposed. By using these new schemes, the solution of an eigenvalue problem on a fine mesh is ...

We present a robust and fast method for the creation of conforming quad layouts on surfaces. Our algorithm is based quantization T-mesh, i.e. an assignment integer lengths to sides non-conforming rectangular partition surface. This representation has benefit being able encode infinite number layout connectivity options in finite manner, which guarantees that valid can always be found. carefully...

In this paper we show that the h-p spectral element method developed in [3,8,9] applies to elliptic problems in curvilinear polygons with mixed Neumann and Dirichlet boundary conditions provided that the Babuska–Brezzi inf–sup conditions are satisfied. We establish basic stability estimates for a non-conforming h-p spectral element method which allows for simultaneous mesh refinement and variab...

Recently, a geometrically nonlinear continuum theory has been developed for the equilibria of martensitic crystals based on elastic energy minimization. For these non-convex functionals, typically no classical solution exists, and minimizing sequences involving Young measures are studied. This paper presents an extensive computational survey of nite-element discretizations designed for this non...