Analysis of Hessian Recovery Methods for Generating Adaptive Meshes

Proceedings, 15th International Meshing Roundtable, Springer-Verlag, pp.163-172, September 17-20 2006

MESHING
RESEARCH
CORNER

15th International Meshing Roundtable
Birmingham, Alabama, U.S.A.
September 17-20, 2006

Konstantin Lipnikov
Los Alamos National Laboratory
lipnikov@lanl.gov

Yuri Vassilevski
Institute of Numerical Mathematics
vasilevs@dodo.inm.ras.ru

Abstract
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 the variational method gives a smaller error.

Download Full Paper (PDF Format)