Finite element derivative interpolation recovery technique and superconvergence
نویسندگان
چکیده
منابع مشابه
Lagrange Interpolation and Finite Element Superconvergence
Abstract. We consider the finite element approximation of the Laplacian operator with the homogeneous Dirichlet boundary condition, and study the corresponding Lagrange interpolation in the context of finite element superconvergence. For ddimensional Qk-type elements with d ≥ 1 and k ≥ 1, we prove that the interpolation points must be the Lobatto points if the Lagrange interpolation and the fin...
متن کاملhp Adaptive finite elements based on derivative recovery and superconvergence
In this paper, we present a new approach to hpadaptive finite element methods. Our a posteriori error estimates and hp-refinement indicator are inspired by the work on gradient/derivative recovery of Bank and Xu [12,13]. For element τ of degree p, R(∂ uhp), the (piece-wise linear) recovered function of ∂ pu is used to approximate |ε|1,τ = |ûp+1−up|1,τ , which serves as our local error indicator...
متن کاملA New Finite Element Gradient Recovery Method: Superconvergence Property
This is the first in a series of papers where a new gradient recovery method is introduced and analyzed. It is proved that the method is superconvergent for translation invariant finite element spaces of any order. The method maintains the simplicity, efficiency, and superconvergence properties of the Zienkiewicz-Zhu patch recovery method. In addition, under uniform triangular meshes, the metho...
متن کاملSuperconvergence in Finite - Element Methods
My research focuses on applied aspects of the calculus of variations and partial differential equations, particularly nonlinear equations arising from physics and chemistry, and numerical analysis and scientific computing, particularly finite-element analysis and numerical methods for interface motion. I have worked on mathematical and numerical problems arising from materials science, such as ...
متن کاملCover interpolation functions and h-enrichment in finite element method
This paper presents a method to improve the generation of meshes and the accuracy of numerical solutions of elasticity problems, in which two techniques of h-refinement and enrichment are used by interpolation cover functions. Initially, regions which possess desired accuracy are detected. Mesh improvment is done through h-refinement for the elements existing in those regions. Total error of th...
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: Applications of Mathematics
سال: 2011
ISSN: 0862-7940,1572-9109
DOI: 10.1007/s10492-011-0030-3