Finite difference weights, spectral differentiation, and superconvergence
نویسندگان
چکیده
منابع مشابه
Calculation of Weights in Finite Difference Formulas∗
The classical techniques for determining weights in finite difference formulas were either computationally slow or very limited in their scope (e.g., specialized recursions for centered and staggered approximations, for Adams–Bashforth-, Adams–Moulton-, and BDF-formulas for ODEs, etc.). Two recent algorithms overcome these problems. For equispaced grids, such weights can be found very convenien...
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 کاملLagrange 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 کاملSuperconvergence of Least-squares Mixed Finite Elements
In this paper we consider superconvergence and supercloseness in the least-squares mixed finite element method for elliptic problems. The supercloseness is with respect to the standard and mixed finite element approximations of the same elliptic problem, and does not depend on the properties of the mesh. As an application, we will derive more precise a priori bounds for the least squares mixed ...
متن کاملSuperconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals
Abstract. Superconvergence of the velocity is established for mimetic finite difference approximations of second-order elliptic problems over h2-uniform quadrilateral meshes. The superconvergence result holds for a full tensor coefficient. The analysis exploits the relation between mimetic finite differences and mixed finite element methods via a special quadrature rule for computing the scalar...
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: Mathematics of Computation
سال: 2014
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2014-02798-1