IJPAM: Volume 76, No. 4 (2012)

A NEW FAMILY OF MIXED FINITE ELEMENT
SPACES ON A CLASS OF DISTORTED HEXAHEDRA

Ji Hyun Kim$^1$, Do Y. Kwak$^2$
Department of Mathematics
Hannam University
133, Ojeong-Dong, Daedeok-Gu, Daejeon 306-791, REPUBLIC OF KOREA
$^2$Department of Mathematical Sciences
KAIST
Daejeon, 305-701, REPUBLIC OF KOREA


Abstract. In this paper, we introduce a new family of mixed finite element spaces for elliptic problem on a domain partitioned by a class of distorted hexahedra. We show an optimal order of approximation for the velocity variable for all $k\geq 0$. For the pressure variable, we suggest a local post-processing technique to obtain an optimal order.

Received: January 20, 2012

AMS Subject Classification: 65N30, 65N12

Key Words and Phrases: mixed finite element method, optimal order, hexahedra, local post-processing technique

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 76
Issue: 4