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Given an unconditionally stable algorithm for solving the Cahn-Hilliard equation, we present a general calculation for an analytic time step $\d \tau$ in terms of an algorithmic time step $\dt$. By studying the accumulative multi-step error…

Materials Science · Physics 2007-05-23 Mowei Cheng , James A. Warren

We derive an exact formula for the complex frequency in spatio-temporal stability analysis that is valid for arbitrary complex wave numbers. The usefulness of the formula lies in the fact that it depends only on purely temporal quantities,…

Fluid Dynamics · Physics 2017-02-08 Lennon O Naraigh , Peter D. M. Spelt

In this paper, we study the mixed element schemes of the Reissner-Mindlin plate model and the Kirchhoff plate model in multiply-connected domains. By a regular decomposition of $H_0({\rm rot},\Omega)$ and a Helmholtz decomposition of its…

Numerical Analysis · Mathematics 2017-02-22 Shuo Zhang

In this paper, we consider a weakly coupled system consisting of a viscoelastic Kirchhoff plate equation involving free boundary conditions and the viscoelastic wave equation with Dirichlet boundary conditions in a bounded domain. By…

Analysis of PDEs · Mathematics 2023-03-17 Zayd Hajjej , Mohammad Akil , Mohamed Balegh , Marcelo Cavalcanti

This study presents the analytical formulation and the finite element solution of fractional order nonlocal plates under both Mindlin and Kirchoff formulations. By employing consistent definitions for fractional-order kinematic relations,…

Computational Engineering, Finance, and Science · Computer Science 2021-02-03 Sansit Patnaik , Sai Sidhardh , Fabio Semperlotti

The work reported in this article presents a high-order, stable, and efficient Gegenbauer pseudospectral method to solve numerically a wide variety of mathematical models. The proposed numerical scheme exploits the stability and the…

Numerical Analysis · Mathematics 2023-03-06 Kareem T. Elgindy

The stability of classical semi-implicit scheme, and some more advanced iterative schemes recently proposed for Numerical Weather Prediction (NWP) purpose is examined. In all these schemes, the solution of the centred-implicit non-linear…

Atmospheric and Oceanic Physics · Physics 2009-11-10 Pierre Benard

The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…

Numerical Analysis · Mathematics 2020-10-28 Zhengqi Zhang , Zhi Zhou

Recent results in the literature provide computational evidence that stabilized semi-implicit time-stepping method can efficiently simulate phase field problems involving fourth-order nonlinear dif- fusion, with typical examples like the…

Numerical Analysis · Mathematics 2016-06-22 Dong Li , Zhonghua Qiao , Tao Tang

In this article, we study the semi discrete and fully discrete formulations for a Kirchhoff type quasilinear integro-differential equation involving time-fractional derivative of order $\alpha \in (0,1) $. For the semi discrete formulation…

Numerical Analysis · Mathematics 2023-05-08 Lalit Kumar , Sivaji Ganesh Sista , Konijeti Sreenadh

In this paper, we study a numerical method for the solution of partial differential equations on evolving surfaces. The numerical method is built on the stabilized trace finite element method (TraceFEM) for the spatial discretization and…

Numerical Analysis · Mathematics 2018-03-23 Christoph Lehrenfeld , Maxim A. Olshanskii , Xianmin Xu

In this work, the propagation of an ultrasonic pulse in a thin plate is computed solving the differential equations modeling this problem. To solve these equations finite differences are used to discretize the temporal variable, while…

This study presents an efficient, accurate, effective and unconditionally stable time stepping scheme for the Darcy-Brinkman equations in double-diffusive convection. The stabilization within the proposed method uses the idea of stabilizing…

Numerical Analysis · Mathematics 2018-04-10 Aytekin Çıbık , Medine Demir , Songul Kaya

We are interested in numerically solving a transitional model derived from the Bloch model. The Bloch equation describes the time evolution of the density matrix of a quantum system forced by an electromagnetic wave. In a high frequency and…

Analysis of PDEs · Mathematics 2023-08-02 Brigitte Bidégaray-Fesquet , Clément Jourdana , Léopold Trémant

The generalized-$\alpha$ method encompasses a wide range of time integrators. The method possesses high-frequency dissipation while minimizing unwanted low-frequency dissipation and the numerical dissipation can be controlled by the user.…

Numerical Analysis · Mathematics 2019-02-15 Quanling Deng , Pouria Behnoudfar , Victor M. Calo

A novel mixed-hybrid method for Kirchhoff-Love shells is proposed that enables the use of classical, possibly higher-order Lagrange elements in numerical analyses. In contrast to purely displacement-based formulations that require higher…

Computational Engineering, Finance, and Science · Computer Science 2026-02-17 Jonas Neumeyer , Michael Wolfgang Kaiser , Thomas-Peter Fries

We aim at the development and analysis of the numerical schemes for approximately solving the backward diffusion-wave problem, which involves a fractional derivative in time with order $\alpha\in(1,2)$. From terminal observations at two…

Numerical Analysis · Mathematics 2021-09-16 Zhengqi Zhang , Zhi Zhou

Several numerical schemes for 3-wave kinetic equations have been proposed in recent work and shown to be accurate and computationally efficient [8,33,34,35]. However, their rigorous numerical analysis remains open. This paper aims to close…

Numerical Analysis · Mathematics 2026-02-03 Minh-Binh Tran , Bangjie Wang

We consider unsteady poroelasticity problem in fractured porous medium within the classical Barenblatt double-porosity model. For numerical solution of double-porosity poroelasticity problems we construct splitting schemes with respect to…

Computational Engineering, Finance, and Science · Computer Science 2016-01-26 A. E. Kolesov , P. N. Vabishchevich

The present work focuses on geometrically exact finite elements for highly slender beams. It aims at the proposal of novel formulations of Kirchhoff-Love type, a detailed review of existing formulations of Kirchhoff-Love and Simo-Reissner…

Computational Engineering, Finance, and Science · Computer Science 2019-05-08 Christoph Meier , Wolfgang A. Wall , Alexander Popp