Simplicial Finite Elements in Higher Dimensions

0089209 - MÚ 2008 RIV CZ eng J - Journal Article
Brandts, J. - Korotov, S. - Křížek, Michal
Simplicial Finite Elements in Higher Dimensions.
[Simpliciální konečné prvky ve vyšších dimenzích.]
Applications of Mathematics. Roč. 52, č. 3 (2007), s. 251-265. ISSN 0862-7940. E-ISSN 1572-9109
R&D Projects: GA ČR GA201/04/1503
Institutional research plan: CEZ:AV0Z10190503
Keywords : n-simplex * finite element method * superconvergence
Subject RIV: BA - General Mathematics

Over the past fifty years, finite element methods for the approximation of solutions of partial differential equations (PDEs) have become a powerful and reliable tool. Theoretically, these methods are not restricted to PDEs formulated on physical domains up to dimension three. Although at present there does not seem to be a very high practical demand for finite element methods that use higher dimensional simplicial partitions, there are some advantages in studying the methods independent of the dimension. For instance, it provides additional insights into the structure and essence of proofs of results in one, two and three dimensions. In this survey paper we review some recent progress in this direction.

V článku uvádíme přehled výsledků týkajících se použití n-rozměrných simplexů v metodě konečných prvků.
Permanent Link: http://hdl.handle.net/11104/0150491