SONDERFORSCHUNGSBEREICH 393: NUMERISCHE SIMULATION AUF MASSIV-PARALLELEN RECHNERN, TECHNISCHE UNIVERSITÄT CHEMNITZ   ]

Meyer, Arnd : Stable evaluation of the Jacobians for curved triangles

Author(s):

Meyer, Arnd

Title:

Stable evaluation of the Jacobians for curved triangles

Electronic source:

application/pdf
application/postscript

Preprint series:

Technische Universität Chemnitz, SFB 393 (Germany), SFB393-Preprint 5, 2003

Mathematics Subject Classification:

65N30			[ Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods ]
65N22			[ Solution of discretized equations ]
65N12			[ Stability and convergence of numerical methods ]

Abstract:

In the adaptive finite element method, the solution of a p.d.e. is approximated from finer and finer meshes, which are controlled by error estimators. So, starting from a given coarse mesh, some elements are subdivided a couple of times. We investigate the question of avoiding instabilities which limit this process from the fact that nodal coordinates of one element coincide in more and more leading digits. In a previous paper the stable calculation of the Jacobian matrices of the element mapping was given for straight line triangles, quadrilaterals and hexahedrons. Here, we generalize this ideas to linear and quadratic triangles on curved boundaries.

Keywords:

adaptive finite element method; Jacobian matrix; stable calculation

Language:

English

Publication time:

3 / 2003