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A new family of high regularity elements
Author(s) -
Sun Jiguang
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20601
Subject(s) - partition of unity , biharmonic equation , mathematics , partition (number theory) , cover (algebra) , finite element method , partial differential equation , basis function , domain (mathematical analysis) , basis (linear algebra) , space (punctuation) , partial derivative , pure mathematics , mathematical analysis , algebra over a field , geometry , computer science , combinatorics , mechanical engineering , physics , engineering , thermodynamics , boundary value problem , operating system
Abstract In this article, we propose a new family of high regularity finite element spaces. The global approximation spaces are obtained in two steps. We first build an open cover of the computational domain and local approximation spaces on each patch of the cover. Then we construct partition of unity functions subordinate to the open cover depending on the regularity requirement. The basis functions of the global space is given by the products of the local basis functions and the corresponding partition of unity functions. The method can be used to construct finite element spaces of any desired regularity. Approximation properties and implementation details are discussed. Numerical examples for the biharmonic equation are presented to show the effectiveness of the proposed method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 28: 1–16, 2012