Results 51 to 60 of about 207 (177)

Error Analysis of a Pressure‐Correction Method With Explicit Time‐Stepping

International Journal for Numerical Methods in Fluids, Volume 97, Issue 10, Page 1363-1378, October 2025.
We study explicit variants of this well‐established pressure‐correction scheme for solving the Navier–Stokes equations. Step 3 is replaced by an explicit time‐integration method. We give the complete error analysis for this scheme that allows for highly efficient implementations.
Utku Kaya, Thomas Richter
wiley   +1 more source

A Hybrid Pressure Formulation of the Face‐Centred Finite Volume Method for Viscous Laminar Incompressible Flows

International Journal for Numerical Methods in Engineering, Volume 126, Issue 10, 30 May 2025.
ABSTRACT This work presents a hybrid pressure face‐centred finite volume (FCFV) solver to simulate steady‐state incompressible Navier‐Stokes flows. The method leverages the robustness, in the incompressible limit, of the hybridisable discontinuous Galerkin paradigm for compressible and weakly compressible flows to derive the formulation of a novel, low‐
Matteo Giacomini, Davide Cortellessa, Luan M. Vieira, Ruben Sevilla, Antonio Huerta   +4 more
wiley   +1 more source

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

Superconvergence of a Nonconforming Interface Penalty Finite Element Method for Elliptic Interface Problems

Axioms
In our previous works, we developed the superconvergence of a nonconforming finite element method based on unfitted meshes for an elliptic interface problem and elliptic problem, respectively.
Xiaoxiao He
doaj   +1 more source

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

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

Superconvergence of Mixed Finite Element Method with Bernstein Polynomials for Stokes Problem

Axioms
In this paper, we employ interpolation and projection methodologies to establish a superconvergence outcome for the Stokes problem, as approximated by the mixed finite element method (FEM) utilizing Bernstein polynomial basis functions.
Lanyin Sun, Siya Wen, Ziwei Dong
doaj   +1 more source

The Backward Euler Fully Discrete Finite Volume Method for the Problem of Purely Longitudinal Motion of a Homogeneous Bar

Abstract and Applied Analysis, 2012
We present a linear backward Euler fully discrete finite volume method for the initial-boundary-value problem of purely longitudinal motion of a homogeneous bar and an give optimal order error estimates in L2 and H1 norms.
Ziwen Jiang, Deren Xie
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

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