Stable evaluation of the Jacobians for curved triangles
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 li...
| Summary: | 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.
|
|---|