Results 61 to 70 of about 207 (177)

Superconvergence of a finite element method for the time-fractional diffusion equation with a time-space dependent diffusivity

Advances in Difference Equations, 2020
In this work, a time-fractional diffusion problem with a time-space dependent diffusivity is considered. The solution of such a problem has a weak singularity at the initial time t = 0 $t=0$ .
Na An
doaj   +1 more source

A Class of Higher‐Order Collocation Scheme for the Integral Equation of the Convolution Type

Journal of Mathematics, Volume 2025, Issue 1, 2025.
Auto convolution Volterra integral equations (ACVIEs) are the particular form of non‐standard integral equations arising in mathematical modeling processes and the computation of certain functions. In this paper, a novel class of multistep collocation methods (NM‐SCMs) is constructed in order to find a higher‐order method is constructed for the ...
M. Alsahlanee, P. Darania, S. Pishbin, Xian-Ming Gu   +3 more
wiley   +1 more source

Superconvergence of the function value for pentahedral finite elements for an elliptic equation with varying coefficients

Boundary Value Problems, 2020
In this article, for an elliptic equation with varying coefficients, we first derive an interpolation fundamental estimate for the P 2 ( x , y ) ⊗ P 2 ( z ) $\mathcal{P}_{2}(x,y)\otimes \mathcal{P}_{2}(z)$ pentahedral finite element over uniform ...
Jinghong Liu, Qiding Zhu
doaj   +1 more source

FFT‐based computational micromechanics with Dirichlet boundary conditions on the rotated staggered grid

International Journal for Numerical Methods in Engineering, Volume 125, Issue 21, 15 November 2024.
Abstract Imposing nonperiodic boundary conditions for unit cell analyses may be necessary for a number of reasons in applications, for example, for validation purposes and specific computational setups. The work at hand discusses a strategy for utilizing the powerful technology behind fast Fourier transform (FFT)‐based computational micromechanics ...
Lennart Risthaus, Matti Schneider
wiley   +1 more source

Orthogonal polynomial bases in the mixed virtual element method

Numerical Methods for Partial Differential Equations, Volume 40, Issue 6, November 2024.
Abstract The use of orthonormal polynomial bases has been found to be efficient in preventing ill‐conditioning of the system matrix in the primal formulation of Virtual Element Methods (VEM) for high values of polynomial degree and in presence of badly‐shaped polygons.
Stefano Berrone, Stefano Scialò, Gioana Teora   +2 more
wiley   +1 more source

Discrete Legendre modified projection-type methods for Hammerstein integral equations

Математичні Студії
We investigate discrete modified projection-type methods for the numerical approximation of nonlinear Hammerstein integral equations with sufficiently smooth kernels.
H. Bouda, C. Allouch, M. Arrai
doaj   +1 more source

Multidomain spectral approach to rational‐order fractional derivatives

Studies in Applied Mathematics, Volume 152, Issue 4, Page 1110-1132, May 2024.
Abstract We propose a method to numerically compute fractional derivatives (or the fractional Laplacian) on the whole real line via Riesz fractional integrals. The compactified real line is divided into a number of intervals, thus amounting to a multidomain approach; after transformations in accordance with the underlying Zq$Z_{q}$ curve ensuring ...
Christian Klein, Nikola Stoilov
wiley   +1 more source

Capturing Multiple Singularities with Spectral Accuracy for Multi-Term Fractional Differential Equations

Mathematics
This paper develops a robust numerical scheme based on a frame collocation method for solving multi-term fractional ordinary differential equations (FODEs) whose solutions exhibit multiple singularities at the origin.
Han Fu, Tinggang Zhao, Benxue Gong
doaj   +1 more source

Superconvergence Analysis of Finite Element Method for a Second-Type Variational Inequality

Journal of Applied Mathematics, 2012
This paper studies the finite element (FE) approximation to a second-type variational inequality. The supe rclose and superconvergence results are obtained for conforming bilinear FE and nonconforming EQrot FE schemes under a reasonable regularity of the
Dongyang Shi, Hongbo Guan, Xiaofei Guan
doaj   +1 more source

Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation

Advances in Difference Equations, 2019
Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation.
Lin He, Juncheng Lv
doaj   +1 more source