Results 41 to 50 of about 207 (177)
International Journal for Numerical Methods in Engineering, Volume 127, Issue 2, 30 January 2026.ABSTRACT FETI‐DP is a mature domain decomposition algorithm that has been successfully applied to different problems, demonstrating impressive performance. To be effective, the algorithm needs to be equipped with different technicalities that somewhat complicate its implementation.
José A. González +4 more
wiley +1 more source
Superconvergence of Modified Nonconforming Cut Finite Element Method for Elliptic Problems
MathematicsIn this work, we aim to explore the superconvergence of a modified nonconforming cut finite element method with rectangular meshes for elliptic problems. Boundary conditions are imposed via the Nitsche’s method.
Xiaoxiao He, Fei Song
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Journal of Function Spaces, Volume 2026, Issue 1, 2026.In the present article, an emerging subdivision‐based technique is developed for the numerical solution of linear Volterra partial integrodifferential equations (LVPIDEs) of order four with a weakly singular kernel. To approximate the spatial derivatives, the basis function of the subdivision scheme is used, whereas the time discretization is done with
Zainab Iqbal +5 more
wiley +1 more source
Collocation Solutions of a Weakly Singular Volterra Integral Equation
Trends in Computational and Applied Mathematics, 2007 The discrete superconvergence properties of spline collocation solutions for a certain Volterra integral equation with weakly singular kernel are analyzed.
T. Diogo, P. Lima
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Superconvergent Perturbation Method in Quantum Mechanics [PDF]
Physical Review Letters, 1995 An analogue of Kolmogorov's superconvergent perturbation theory in classical mechanics is constructed for self adjoint operators. It is different from the usual Rayleigh--Schrödinger perturbation theory and yields expansions for eigenvalues and eigenvectors in terms of functions of the perturbation parameter.
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A Conforming Least Squares Approach for the Numerical Approximation of Parabolic Equations
Proceedings in Applied Mathematics and Mechanics, Volume 25, Issue 4, December 2025.ABSTRACT We propose a least squares formulation for the numerical approximation of parabolic partial differential equations, which minimizes the residual of the equation using the natural L2(0,T;H−1(Ω))$L^2(0,T;H^{-1}(\Omega))$ norm. In particular, we avoid making regularity assumptions on the problem's data.
Michael Hinze +2 more
wiley +1 more source
Improved Numerical Robustness of the X‐FFT Solver via Internal Scaling
Proceedings in Applied Mathematics and Mechanics, Volume 25, Issue 4, December 2025.ABSTRACT The recently introduced X‐FFT solver improves the spatial accuracy of FFT‐based homogenization methods for two‐dimensional thermal homogenization problems without compromising their numerical efficiency. Through the use of an X‐FEM discretization, optimal error convergence rates of the discretization error are achieved, and the developed X‐FFT
Flavia Gehrig, Matti Schneider
wiley +1 more source
A Priori Error Bounds for the Approximate Deconvolution Leray Reduced Order Model
Numerical Methods for Partial Differential Equations, Volume 41, Issue 6, November 2025.ABSTRACT The approximate deconvolution Leray reduced order model (ADL‐ROM) uses spatial filtering to increase the ROM stability, and approximate deconvolution to increase the ROM accuracy. In the under‐resolved numerical simulation of convection‐dominated flows, ADL‐ROM was shown to be significantly more stable than the standard ROM and more accurate ...
Ian Moore +3 more
wiley +1 more source
Iterated Crank–Nicolson Method for Peridynamic Models
DynamicsIn this paper, we explore the iterated Crank–Nicolson (ICN) algorithm for the one-dimensional peridynamic model. The peridynamic equation of motion is an integro-differential equation that governs structural deformations such as fractures. The ICN method
Jinjie Liu +2 more
doaj +1 more source
Superconvergence for multistep collocation [PDF]
Mathematics of Computation, 1989 One-step collocation methods are known to be a subclass of implicit Runge-Kutta methods. Further, one-leg methods are special multistep one-point collocation methods. In this paper we extend both of these collocation ideas to multistep collocation methods with k previous meshpoints and
Lie, Ivar, Nørsett, Syvert P.
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