Simplicial Partitions with Applications to the Finite Element Method by Jan Brandts & Sergey Korotov & Michal Křížek

Author:Jan Brandts & Sergey Korotov & Michal Křížek
Language: eng
Format: epub
ISBN: 9783030556778
Publisher: Springer International Publishing

form a face-to-face partition which will be said to form the red refinement of . In this case the permutation is the identity. The partition contains subsimplices (see Fig. 8.5 for ).

8.4 Refinements into Path-Tetrahedra

First, we will present the following elementary property.

Lemma 8.2

Let O be the circumcenter of a tetrahedron T. Let P be the circumcenter of a face F of T. If then the line segment PO is perpendicular to the plane containing F.

Proof

The set of all points which have the same distance to all three vertices of F is a straight line perpendicular to the plane containing F. Obviously, both O and P lie on this line.

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