The invertibility of the isoparametric mappings for triangular quadratic Lagrange finite elements

Comparison of some isoparametric mappings for curved triangular spectral elements

The invertibility of the isoparametric mapping for pyramidal and prismatic finite elements

We consider the isoparametric transformation, which maps a given reference element onto a global element given by its vertices, for multi-linear nite elements on pyramids and prisms. We present easily computable conditions on the position of the vertices, which ensure that the isoparametric transformation is bijective.

The Invertibility of the Isoparametric Mapping for Pyramidal and Prismatic Nite Elements

We consider the isoparametric transformation, which maps a given reference element onto a global element given by its vertices, for multi-linear nite elements on pyramids and prisms. We present easily computable conditions on the position of the vertices, which ensure that the isoparametric transformation is bijective.

Maximum norm error estimates in the finite element method with isoparametric quadratic elements and numerical integration

— We consider a second order real elliptic Dirichlet problem in a bounded plane smooth domain, Lu = f in fi œ Ry u — 0 on dQ. For its numerical solution we employ the finite element method with quadratic triangular isoparametric éléments combined with a numerical intégration procedure involving function values at three nodal points in each element. We prove that iffhas third order derivatives i...

On Interpolation Errors over Quadratic Nodal Triangular Finite Elements

Interpolation techniques are used to estimate function values and their derivatives at those points for which a numerical solution of any equation is not explicitly evaluated. In particular, the shape functions are used to interpolate a solution (within an element) of a partial differential equation obtained by the finite element method. Mesh generation and quality improvement are often driven ...