In this paper we introduce a new mesh refinement method for subdivision surfaces. It generates a semiregular 4-direction hierarchical structure from control meshes representing 2D manifolds of arbitrary topology. The main advantage of this structure is that it allows the extraction of conforming variable-resolution meshes based on spatially varying adaptation functions. We also present a smooth...

We consider conforming finite element (FE) approximations for the time-dependent Oberbeck-Boussinesq model with inf-sup stable pairs for velocity and pressure and use a stabilization of the incompressibility constraint. In case of dominant convection, a local projection stabilization (LPS) method in streamline direction is considered both for velocity and temperature. For the arising nonlinear ...

In this paper, we consider a two-dimensional parabolic equation with two small parameters. These small parameters make the underlying problem containing multiple scales over the whole problem domain. By using the maximum principle with carefully chosen barrier functions, we obtain the pointwise derivative estimates of arbitrary order, from which an anisotropic mesh is constructed. This mesh use...

This paper describes an automatic and efficient approach to construct unstructured tetrahedral and hexahedral meshes for a composite domain made up of heterogeneous materials. The boundaries of these material regions form non-manifold surfaces. In earlier papers, we developed an octree-based isocontouring method to construct unstructured 3D meshes for a single-material (homogeneous) domain with...

The applicability of the meshing framework ViennaMesh for finite element simulations is investigated. Meshing tools are highly diverse, meaning that each software package offers specific properties, such as the conforming Delaunay property. The feasibility of these properties tends to be domain specific, thus restricting the general application of ameshing tool. For research purposes, it is des...

We consider robust iterative methods for discontinuous Galerkin (DG) H(div,Ω)conforming discretizations of the Brinkman equations. We describe a simple Uzawa iteration for the solution of this problem, which requires the solution of a nearly incompressible linear elasticity type equation with mass term on every iteration. We prove the uniform stability of the DG discretization for both problems...

The subject of the paper is the analysis of error estimates of the combined nite volume-nite element method for the numerical solution of a scalar nonlinear conservation law equation with a diiusion term. Nonlinear convective terms are approximated with the aid of a monotone nite volume scheme considered over the nite volume mesh dual to a triangular grid, whereas the diiusion term is discretiz...

This paper addresses fully space-time adaptive magnetic field computations. We describe an adaptive Whitney finite element method for solving the magnetoquasistatic formulation of Maxwell’s equations on unstructured 3D tetrahedral grids. Spatial mesh refinement and coarsening are based on hierarchical error estimators especially designed for combining tetrahedral H(curl)-conforming edge element...

A non-stabilized mixed discontinuous Galerkin method for the discretization of the Maxwell operator on simplicial meshes is studied. In contrast to the stabilized scheme introduced in [7], the proposed formulation contains no normal– jump stabilization; instead, it is based on discontinuous mixed-order (P) − P elements for the approximation of the unknowns. A priori error bounds in the energy n...