Results 81 to 90 of about 1,836 (211)

Natural superconvergence points for splines

CoRR
This paper develops a unified theory of natural superconvergence points for polynomial spline approximations to second-order elliptic problems. Beginning with the one-dimensional case, we establish that when a point $x_0$ is a local symmetric center of the partition, the numerical error $(u-u_h)^{(s)}(x_0)$ exhibits superconvergence whenever the ...
Peng Yang, Zhimin Zhang
openaire   +2 more sources

A Chemo‐Damage‐Mechanical Coupled Phase‐Field Model for Three‐Dimensional Hydrogen‐Assisted Dynamic Cracking

International Journal for Numerical Methods in Engineering, Volume 126, Issue 8, 30 April 2025.
ABSTRACT This study develops a chemo‐damage‐mechanical coupled phase‐field method for modeling two‐dimensional and/or three‐dimensional hydrogen‐assisted transient dynamic cracking in metallic materials. In this method, hydrogen diffusion in solids is described by the evolution of bulk hydrogen concentration governed by the diffusion equation with an ...
Hui Li, Shanyong Wang
wiley   +1 more source

An X‐FFT Solver for Two‐Dimensional Thermal Homogenization Problems

International Journal for Numerical Methods in Engineering, Volume 126, Issue 7, 15 April 2025.
ABSTRACT We introduce an approach to computational homogenization which unites the accuracy of interface‐conforming finite elements (FEs) and the computational efficiency of methods based on the fast Fourier transform (FFT) for two‐dimensional thermal conductivity problems.
Flavia Gehrig, Matti Schneider
wiley   +1 more source

An improved finite element approximation and superconvergence for temperature control problems

Mathematical Modelling and Analysis, 2013
In this paper, we consider an improved finite element approximation for temperature control problems, where the state and the adjoint state are discretized by piecewise linear functions while the control is not discretized directly.
Yuelong Tang
doaj   +1 more source

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

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

Convergence of Damped Polarization Schemes for the FFT‐Based Computational Homogenization of Inelastic Media With Pores

International Journal for Numerical Methods in Engineering, Volume 126, Issue 3, 15 February 2025.
ABSTRACT Porous microstructures represent a challenge for the convergence of FFT‐based computational homogenization methods. In this contribution, we show that the damped Eyre–Milton iteration is linearly convergent for a class of nonlinear composites with a regular set of pores, provided the damping factor is chosen between zero and unity.
Elodie Donval, Matti Schneider
wiley   +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 differential structure for finite element methods on perturbed surface meshes [PDF]

Superconvergence of differential structure on discretized surfaces is studied in this paper. The newly introduced geometric supercloseness provides us with a fundamental tool to prove the superconvergence of gradient recovery on deviated surfaces.
Guo, Ting, Dong, Guozhi, Guo, Hailong
core   +2 more sources

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