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Upper bound limit analysis allows one to evaluate directly the ultimate load of structures without performing a cumbersome incremental analysis. In order to numerically apply this method to thin plates in bending, several authors have…

Numerical Analysis · Mathematics 2014-10-02 Jérémy Bleyer , Guillaume Carlier , Vincent Duval , Jean-Marie Mirebeau , Gabriel Peyré

The coupled cluster method (CCM) is a method of quantum many-body theory that may provide accurate results for the ground-state properties of lattice quantum spin systems even in the presence of strong frustration and for lattices of…

Strongly Correlated Electrons · Physics 2009-11-11 D. J. J. Farnell , J. Schulenburg , J. Richter , K. A. Gernoth

We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point…

Numerical Analysis · Mathematics 2025-10-21 Xiaowen Gan , Yuqian Teng , Sisheng Wang

We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries are…

Numerical Analysis · Mathematics 2021-11-24 Tuan Anh Dao , Ken Mattsson , Murtazo Nazarov

In this paper, we rigorously study an order 2 scheme that was previously proposed by some of the authors. A slight modification is proposed that enables us to prove the convergence of the scheme while simplifying in the same time the inner…

Numerical Analysis · Mathematics 2015-06-05 François Alouges , Evaggelos Kritsikis , Jutta Steiner , Jean-Christophe Toussaint

We introduce an integral representation of the Monge-Amp\`ere equation, which leads to a new finite difference method based upon numerical quadrature. The resulting scheme is monotone and fits immediately into existing convergence proofs…

Numerical Analysis · Mathematics 2022-12-01 Jake Brusca , Brittany Froese Hamfeldt

In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…

In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase…

Analysis of PDEs · Mathematics 2019-02-20 Pierluigi Colli , Gianni Gilardi , Pavel Krejčí , Paolo Podio-Guidugli , Jürgen Sprekels

We introduce and analyze a robust nonconforming finite element method for a three dimensional singularly perturbed quad-curl model problem. For the solution of the model problem, we derive proper a priori bounds, based on which, we prove…

Numerical Analysis · Mathematics 2022-06-27 Baiju Zhang , Zhimin Zhang

This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…

Numerical Analysis · Mathematics 2021-11-23 Toni Sayah

In this work, we develop an adaptive nonconforming finite element algorithm for the numerical approximation of phase-field parameterized topology optimization governed by the Stokes system. We employ the conforming linear finite element…

Numerical Analysis · Mathematics 2026-04-20 Bangti Jin , Jing Li , Yifeng Xu , Shengfeng Zhu

We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…

Optimization and Control · Mathematics 2024-06-04 Jochen Schmid , Philipp Seufert , Michael Bortz

A high-order combined interpolation/finite element technique is developed for solving the coupled groundwater-surface water system that governs flows in karst aquifers. In the proposed high-order scheme we approximate the time derivative…

Numerical Analysis · Mathematics 2025-05-28 Eric Ngondiep , Areej A. Binsultan , Ibtisam M. Aldawish

In this paper we discuss a hybridised method for FEM-BEM coupling. The coupling from both sides use a Nitsche type approach to couple to the trace variable. This leads to a formulation that is robust and flexible with respect to…

Numerical Analysis · Mathematics 2022-03-22 Timo Betcke , Michał Bosy , Erik Burman

We study the numerical solution of a Cahn-Hilliard/Allen-Cahn system with strong coupling through state and gradient dependent non-diagonal mobility matrices. A fully discrete approximation scheme in space and time is proposed which…

Numerical Analysis · Mathematics 2024-08-02 Aaron Brunk , Herbert Egger , Oliver Habrich

Classical atomistic simulations based on interatomic potentials resolve lattice instabilities, defect nucleation, and microstructure evolution with high fidelity, but their accessible system sizes remain far below those required for…

Numerical Analysis · Mathematics 2026-05-26 Aagashram Neelakandan , Karsten Albe , Bernhard Eidel

In this paper, we propose a novel high order unfitted finite element method on Cartesian meshes for solving the acoustic wave equation with discontinuous coefficients having complex interface geometry. The unfitted finite element method…

Numerical Analysis · Mathematics 2023-02-06 Zhiming Chen , Yong Liu , Xueshuang Xiang

A heterogeneous Cauchy elastic material may display micromechanical effects that can be modeled in a homogeneous equivalent material through the introduction of higher-order elastic continua. Asymptotic homogenization techniques provide an…

Computational Physics · Physics 2018-04-20 A. Bacigalupo , M. Paggi , F. Dal Corso , D. Bigoni

The fourth-order PDE that models the density variation of smectic A liquid crystals presents unique challenges in its (numerical) analysis beyond more common fourth-order operators, such as the classical biharmonic. While the operator is…

Numerical Analysis · Mathematics 2023-08-24 Patrick E. Farrell , Abdalaziz Hamdan , Scott P. MacLachlan

We present a higher order space-time unfitted finite element method for convection-diffusion problems on coupled (surface and bulk) domains. In that way, we combine a method suggested by Heimann, Lehrenfeld, Preu{\ss} (SIAM J. Sci. Comput.…

Numerical Analysis · Mathematics 2025-04-28 Fabian Heimann