High order local approximations to derivatives in the finite element method
نویسندگان
چکیده
منابع مشابه
Analysis of High-order Approximations by Spectral Interpolation Applied to One- and Two-dimensional Finite Element Method
The implementation of high-order (spectral) approximations associated with FEM is an approach to overcome the difficulties encountered in the numerical analysis of complex problems. This paper proposes the use of the spectral finite element method, originally developed for computational fluid dynamics problems, to achieve improved solutions for these types of problems. Here, the interpolation n...
متن کاملHigh-Order Local Rate of Convergence By Mesh-Refinement in the Finite Element Method
We seek approximations of the solution u of the Neumann problem for the equation Lu = f in Q with special emphasis on high-order accuracy at a given point x0 e Q. Here ß is a bounded domain in R (N > 2) with smooth boundary, and L is a second-order, uniformly elliptic, differential operator with smooth coefficients. An approximate solution uh is determined by the standard Galerkin method in a s...
متن کاملHigh Order Extended Finite Element Method for Cracked Domains
Computer simulation of fracture processes remains a challenge for many industrial modelling problems. In a classical finite element method, the non-smooth displacement near the crack tip is captured by refining the mesh locally. The number of degrees of freedom may drastically increase, especially in three dimensional applications. Moreover, the incremental computation of a crack growth needs f...
متن کاملA High-order Finite Element Method for Electrical Impedance Tomography
Electrical impedance tomography (EIT) is a non-invasive imaging technique where a conductivity distribution in a domain is reconstructed from boundary voltage measurements. The voltage data are generated by injecting currents into the domain. This is an ill-conditioned non-linear inverse problem. Small measurement or forward modeling errors can lead to unbounded fluctuations in the reconstructi...
متن کاملHigh-Order Multiscale Finite Element Method for Elliptic Problems
In this paper, a new high-order multiscale finite element method is developed for elliptic problems with highly oscillating coefficients. The method is inspired by the multiscale finite element method developed in [3], but a more explicit multiscale finite element space is constructed. The approximation space is nonconforming when oversampling technique is used. We use a PetrovGalerkin formulat...
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: 1977
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1977-0438664-4