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On numerical regularity of the face-to-face longest-edge bisection algorithm for tetrahedral partitions
The finite element method usually requires regular or strongly regular families of partitions in order to get guaranteed a priori or a posteriori error estimates. In this paper we examine the recently invented longest-edge ...
Red refinements of simplices into congruent subsimplices
We show that in dimensions higher than two, the popular "red refinement" technique, commonly used for simplicial mesh refinements and adaptivity in the finite element analysis and practice, never yields subsimplices which ...
On nonobtuse refinements of tetrahedral finite element meshes
It is known that piecewise linear continuous finite element (FE) approximations on nonobtuse tetrahedral FE meshes guarantee the validity of discrete analogues of various maximum principles for a wide class of elliptic ...