Global and local refinement techniques yielding nonobtuse tetrahedral partitions

Preservation of basic qualitative properties (for example, the maximum principle) ofthe solution of partial differential equations by its finite-element approximations is an important goal in mathematical modelling and simulation. Nonobtuse tetrahedral partitions and linear finite elements guarantee the validity of the discrete analogues of the maximum principle for a wide class of parabolic and elliptic problems. In order to get more accurate approximation, we often need to refine the used partitions globally or locally. In this paper, we first propose two variants of global refinement techniques, which produce nonobtuse face-to-face tetrahedral partitions. Second, we present a new local refinement technique which generates nonobtuse face-to-face tetrahedral partitions in a neighbourhood of a given vertex.