Michal Křížek

On the maximum angle condition for linear tetrahedral elements

Synge’s maximum angle condition for triangular elements is generalized to tetrahedral elements. For the generalized condition, it is proved that tetrahedra may degenerate in a certain way and the error of the standard linear interpolation remains

Superconvergence phenomenon in the finite element method arising from averaging gradients

O(h)

On Nonobtuse Simplicial Partitions

in the

On a global superconvergence of the gradient of linear triangular elements

W_p^1 (\Omega )

Mathematical and numerical modelling in electrical engineering theory and applications

-norm for sufficiently smooth functions and

Second-order optimality conditions for nondominated solutions of multiobjective programming with

p \in [1,\infty ]

C^{1,1}

.

data

SummaryWe study a superconvergence phenomenon which can be obtained when solving a 2nd order elliptic problem by the usual linear elements. The averaged gradient is a piecewise linear continuous vector field, the value of which at any nodal point is an average of gradients of linear elements on triangles incident with this nodal point. The convergence rate of the averaged gradient to an exact gradient in theL2-norm can locally be higher even by one than that of the original piecewise constant discrete gradient.

On a Connection of Number Theory with Graph Theory

This paper surveys some results on acute and nonobtuse simplices and associated spatial partitions. These partitions are relevant in numerical mathematics, including piecewise polynomial approximation theory and the finite element method. Special attention is paid to a basic type of nonobtuse simplices called path-simplices, the generalization of right triangles to higher dimensions. In addition to applications in numerical mathematics, we give examples of the appearance of acute and nonobtuse simplices in other areas of mathematics.

The maximum angle condition is not necessary for convergence of the finite element method

Abstract We study a simple superconvergent scheme which recovers the gradient when solving a second-order elliptic problem in the plane by the usual linear elements. The recovered gradient globally approximates the true gradient even by one order of accuracy higher in the L 2 -norm than the piecewise constant gradient of the Ritz—Galerkin solution. A superconvergent approximation to the boundary flux is presented as well.