A higher-order mimetic method for the solution of partial differential equations on unstructured meshes is developed and demonstrated on the problem of conductive heat transfer. Mimetic discretization methods create discrete versions of the partial differential operators (such and the gradient and divergence) that are exact in some sense and therefore mimic the important mathematical properties...

In [3] have been constructed very high order residual distribution schemes for scalar problems. They were using triangle unstructured meshes. However, the construction was quite involved and was not very flexible. Here, following [1], we develop a systematic way of constructing very high order non oscillatory schemes for such meshes. Applications to scalar and systems problems are given.

This paper presents a generic approach to generation of surface and volume unstructured meshes for complex free-form objects, obtained by laser scanning. A four-stage automated procedure is proposed for discrete data sets: surface mesh extraction from Delaunay tetrahedrization of scanned points, surface mesh simplification, definition of triangular interpolating subdivision faces, Delaunay volu...

Partial differential equations in complex domains are very flexibly discretized by 7 finite elements with unstructured meshes. For such problems, the challenging task to construct 8 coarse level spaces for efficient multilevel preconditioners can in many cases be solved by a 9 semi-geometric approach, which is based on a hierarchy of non-nested meshes. In this paper, 10 we investigate the conne...

New mimetic discretizations of diffusion-type equations (for instance, equations modeling single phase Darcy flow in porous media) on unstructured polygonal meshes are derived. The first order convergence rate for the fluid velocity and the second-order convergence rate for the pressure on polygonal, locally refined and non-matching meshes are demonstrated with numerical experiments.

The polynomial preserving recovery (PPR) is used to enhance the finite element eigenvalue approximation. Remarkable fourth order convergence is observed for linear elements under structured meshes as well as unstructured initial meshes (produced by the Delaunay triangulation) with the conventional bisection refinement.

A parallel tetrahedral mesh adaptation code is expanded to treat general, mixed-element unstructured meshes comprised of any combination of basic element types. Emphasis is placed on developing conforming mesh modification methods that are solver-independent. Specific developments include the implementation of a treatment for viscous, high aspect ratio near wall tetrahedra, and cell subdivision...

A new Discrete Ordinates transport solver for unstructured tetrahedral meshes is presented. The uses the Discontinuous Galërkin Finite Element Method with linear or quadratic expansion of flux within each cell. solution one-group problem obtained non-preconditioned fixed-point GMRES iterations. Precision and performances are evaluated on 3D Radiation Transport Benchmark Problems proposed by Kob...