6 papers
Generalization of Strang-Fix remark for discrete maximum principles on tetrahedral meshes
Safdar Ali, Maksat Ashyraliyev, Sergey Korotov +1
Most of qualitative properties of finite element (FE) approximations for various PDE models, in particular the validity of the discrete maximum principles (DMPs), are usually guara…
On degeneration of tetrahedra under longest-edge n-section refinement
Sergey Korotov
For every integer , we construct explicit tetrahedral counterexamples showing that repeated longest-edge (LE) n-section refinement does not, in general, preserve shape reg…
The longest-edge bisection algorithm may produce degenerating tetrahedra
Sergey Korotov
An explicit sequence of tetrahedra generated by the longest-edge bisection algorithm is shown to degenerate. The example violates shape regularity and both the minimum- and maximum…
On Triangulations Generated by the Largest-Angle -Section Algorithm
Jérôme Michaud, Sergey Korotov
We define a mesh refinement algorithm based on the rule of dividing the largest angles of triangular elements of planar partitions in focus into equal parts, and analyse the (g…
Dynamics of the Longest-Edge Altitude Bisection Algorithm
Jérôme Michaud, Sergey Korotov
We study a longest-edge based refinement scheme for triangulations, termed the longest-edge altitude bisection (LEAB), in which each triangle is subdivided by dropping the altitude…
On the Orbits of Similarity Classes of Tetrahedra Generated by the Longest-Edge Bisection Algorithm
Jérôme Michaud, Sergey Korotov
In this work, we study the dynamics of similarity classes of tetrahedra generated by the longest-edge bisection (LEB) algorithm. Building on the normalization strategy introduced b…