Applicability of the Bramble-Hilbert lemma in interpolation problems of narrow quadrilateral isoparametric finite elements
نویسندگان
چکیده
منابع مشابه
The Bramble-hilbert Lemma *
In numerical analysis, the Bramble-Hilbert lemma bounds the error of an approximation of a function u by a polynomial of order at most m− 1 in terms of derivatives of u of order m. Both the error of the approximation and the derivatives of u are measured by L norms on a bounded domain in R. This is similar to classical numerical analysis, where, for example, the error of interpolation u on an i...
متن کاملThe Bramble-Hilbert Lemma for Convex Domains
The Bramble-Hilbert lemma is a fundamental result on multivariate polynomial approximation. It is frequently applied in the analysis of Finite Element Methods (FEM) used for numerical solutions of PDEs. However, this classical estimate depends on the geometry of the domain and may ‘blow-up’ for simple examples such as a sequence of triangles of equivalent diameter that become thinner and thinne...
متن کاملAn inverse transformation for quadrilateral isoparametric elements" Analysis and application
The coordinate transformation for quadrilateral isoparametric elements is well-defined in the finite element literature. However, a corresponding inverse transformation is not found. In fact, it has been commonly believed that no explicit solutions to the inverse transformation problem exist. This paper shows that if geometric considerations are used, a complete set of general solutions to the ...
متن کاملError Estimates for Low-Order Isoparametric Quadrilateral Finite Elements for Plates
This paper deals with the numerical approximation of the bending of a plate modeled by Reissner-Mindlin equations. It is well known that, in order to avoid locking, some kind of reduced integration or mixed interpolation has to be used when solving these equations by finite element methods. In particular, one of the most widely used procedures is based on the family of elements called MITC (mix...
متن کاملNew Quadrilateral Mixed Finite Elements
In this paper, we introduce a new family of mixed finite element spaces of higher order (k ≥ 1) on general quadrilateral grids. A typical element has two fewer degrees of freedom than the well-known RaviartThomas finite element RT[k], yet enjoys an optimal-order approximation for the velocity in L 2-norm. The order of approximation in the divergence norm is one less than the velocity, as is com...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1995
ISSN: 0377-0427
DOI: 10.1016/0377-0427(95)00053-4