A Numerical Study of Some Hessian Recovery Techniques on Isotropic and Anisotropic Meshes

Analysis of Hessian Recovery Methods for Generating Adaptive Meshes

We study adaptive meshes which are quasi-uniform in a metric generated by the Hessian of a P1 finite element function. We consider three most efficient methods for recovering this Hessian, one variational method and two projection methods. We compare these methods for problems with anisotropic singularities to show that all Hessian recovery methods result in acceptable adaptive meshes although ...

Families of Meshes Minimizing P 1 Interpolation Error

For a given function, we consider a problem of minimizing the P1 interpolation error on a set of triangulations with a fixed number of triangles. The minimization problem is reformulated as a problem of generating a mesh which is quasi-uniform in a specially designed metric. For functions with indefinite Hessian, we show existence of a family of metrics with highly diverse properties. The famil...

A Stabilized Finite Element Scheme for the Navier-stokes Equations on Quadrilateral Anisotropic Meshes

It is well known that the classical local projection method as well as residual-based stabilization techniques, as for instance streamline upwind Petrov-Galerkin (SUPG), are optimal on isotropic meshes. Here we extend the local projection stabilization for the Navier-Stokes system to anisotropic quadrilateral meshes in two spatial dimensions. We describe the new method and prove an a priori err...

Ani2D Version 1.1 Generator of Anisotropic Meshes based on the Hessian Recovery User’s Guide

Anisotropic Mesh Adaptation for the Finite Element Solution of Anisotropic Diffusion Problems

Anisotropic diffusion problems arise in many fields of science and engineering and are modeled by partial differential equations (PDEs) or represented in variational formulations. Standard numerical schemes can produce spurious oscillations when they are used to solve those problems. A common approach is to design a proper numerical scheme or a proper mesh such that the numerical solution satis...