Symbolic-Numerical Algorithm for Generating Interpolation Multivariate Hermite Polynomials of High-Accuracy Finite Element Method

2017 ◽  
pp. 134-150 ◽  
Author(s):  
A. A. Gusev ◽  
V. P. Gerdt ◽  
O. Chuluunbaatar ◽  
G. Chuluunbaatar ◽  
S. I. Vinitsky ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Algorithm ◽  
Hermite Polynomials ◽  
High Accuracy ◽  
Element Method

A Parameter Robust Finite Element Method for Fourth Order Singularly Perturbed Problems

2017 ◽  
Vol 17 (2) ◽  
pp. 337-349 ◽  
Author(s):  
Christos Xenophontos
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fourth Order ◽  
Hermite Polynomials ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
The Finite Element Method ◽  
Singularly Perturbed Problems ◽  
Exponentially Graded ◽  
Element Method

AbstractWe consider fourth order singularly perturbed problems in one-dimension and the approximation of their solution by the h version of the finite element method. In particular, we use piecewise Hermite polynomials of degree ${p\geq 3}$ defined on an exponentially graded mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at the optimal rate when the error is measured in both the energy norm and a stronger, ‘balanced’ norm. Finally, we illustrate our theoretical findings through numerical computations, including a comparison with another scheme from the literature.

scholarly journals Construction of Multivariate Interpolation Hermite Polynomials for Finite Element Method

2020 ◽  
Vol 226 ◽  
pp. 02007
Author(s):  
Galmandakh Chuluunbaatar ◽  
Alexander A. Gusev ◽  
Ochbadrakh Chuluunbaatar ◽  
Vladimir P. Gerdt ◽  
Sergue I. Vinitsky ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Hermite Polynomials ◽  
Analytical Form ◽  
Multivariate Interpolation ◽  
Partial Derivatives ◽  
Helmholtz Problem ◽  
Finite Element Schemes ◽  
Element Method

A new algorithm for constructing multivariate interpolation Hermite polynomials in analytical form in a multidimensional hypercube is presented. These polynomials are determined from a specially constructed set of values of the polynomials themselves and their partial derivatives with continuous derivatives up to a given order on the boundaries of the finite elements. The effciency of the finite element schemes, algor thms and programs is demonstrated by solving the Helmholtz problem for a cube.

scholarly journals High-accuracy analysis of finite-element method for two-term mixed time-fractional diffusion-wave equations

2018 ◽  
Vol 48 (7) ◽  
pp. 871-887 ◽  
Author(s):  
Yabing WEI ◽  
Yanmin ZHAO ◽  
Yifa TANG ◽  
Fenling WANG ◽  
Zhengguang SHI ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Equations ◽  
Fractional Diffusion ◽  
High Accuracy ◽  
Accuracy Analysis ◽  
Diffusion Wave ◽  
Element Method
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