We develop a Discrete Duality Finite Volume (DDFV) method for the three-dimensional steady Stokes problem with a variable viscosity coefficient on polyhedral meshes. Under very general assumptions on the mesh, which may admit non-convex and non-conforming polyhedrons, we prove the stability and well-posedness of the scheme. We also prove the convergence of the numerical approximation to the vel...

New algorithms are proposed for the modification of a mixed hexahedra-tetrahedra element mesh to maintain compatibility by the insertion of pyramid elements. Several methods for generation of the p+yramidsare presented involving local tetrahedral transformations and’or node insertion near the he.titet interface. Local smoothing and topological operations improve the quality of the transition re...

We apply geometric multigrid methods for the finite element approximation of flow problems governed by Darcy and Brinkman systems used in modeling highly heterogeneous porous media. The method is based on divergence-conforming discontinuous Galerkin methods and overlapping, patch based domain decomposition smoothers. We show in benchmark experiments that the method is robust with respect to mes...

A practical incremental refinement algorithm for computing a quality, conforming Delaunay mesh of an arbitrary 3D piecewise linear complex is given. The algorithm allows small input angles and does not require the local feature size of the input to be computed before performing the refinement. Small input angles are protected with a new type of collar which is simpler to implement and analyze t...

Dedicated to Olof B. Widlund on the occasion of his 60th birthday. Summary. It is shown that for elliptic boundary value problems of order 2m the condition number of the Schur complement matrix that appears in nonoverlapping domain decomposition methods is of order d ?1 h ?2m+1 , where the parameter d measures the diameters of the subdomains and h is the mesh size of the triangulation. The resu...

In this paper, we present an additive Neumann-Neumann type parallel method for solving the system of algebraic equations arising from the mortar finite element discretization of a plate problem on a nonconforming mesh. Locally, we use a conforming Hsieh-CloughTocher macro element in the subdomains. The proposed method is almost optimal i.e. the condition number of the preconditioned problem gro...

In the last decade, non-conforming domain decomposition methods such as the mortar finite element method have been shown to be reliable techniques for several engineering applications that often employ complex finite element design. With this technique, one can conveniently assemble local subcomponents into a global domain without matching the finite element nodes of each subcomponent at the co...

In this paper, we introduce a mixed finite element method on a staggered mesh for the numerical solution of the steady state Navier-Stokes equations in which the two components of the velocity and the pressure are defined on three different meshes. This method is a conforming quadrilateral Q1 × Q1 − P0 element approximation for the Navier-Stokes equations. First-order error estimates are obtain...

The main goal of this project is to develop a parallel tetrahedral mesh generator based on existing sequential mesh generation software. As sequential mesh generation software, the Netgen mesh generator was used due to its availability as LGPL open source software and its wide user base. Parallel mesh generation routines were developed using the MPI libraries and the C++ language. The parallel ...

Abstract We consider mixed finite element approximations of viscous, plastic Bingham flow in a cylindrical pipe. A novel priori and posteriori error analysis is introduced which based on discrete mesh dependent norm for the normalized Lagrange multiplier. This allows proving stability various conforming elements. Numerical examples are presented to support theory demonstrate adaptive refinement.