English
Related papers

Related papers: Finite element approximations of minimal surfaces:…

200 papers

An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…

Numerical Analysis · Mathematics 2021-03-16 Tim Binz , Balázs Kovács

We propose a novel early-terminating mesh refinement strategy using an integrated residual method to solve dynamic feasibility problems. As a generalization of direct collocation, the integrated residual method is used to approximate an…

Optimization and Control · Mathematics 2024-03-13 Eduardo M. G. Vila , Eric C. Kerrigan , Paul Bruce

A type of adaptive finite element method for the eigenvalue problems is proposed based on the multilevel correction scheme. In this method, adaptive finite element method to solve eigenvalue problems involves solving associated boundary…

Numerical Analysis · Mathematics 2012-01-12 Hehu Xie

We present an optimization procedure for generic polygonal or polyhedral meshes, tailored for the Virtual Element Method (VEM). Once the local quality of the mesh elements is analyzed through a quality indicator specific to the VEM, groups…

Numerical Analysis · Mathematics 2024-11-08 Tommaso Sorgente , Stefano Berrone , Silvia Biasotti , Gianmarco Manzini , Michela Spagnuolo , Fabio Vicini

A general adaptive refinement strategy for solving linear elliptic partial differential equation with random data is proposed and analysed herein. The adaptive strategy extends the a posteriori error estimation framework introduced by…

Numerical Analysis · Mathematics 2022-08-23 Alex Bespalov , David Silvester , Feng Xu

We present an efficient mixed finite element method to solve the fourth-order thin film flow equations using moving mesh refinement. The moving mesh strategy is based on harmonic mappings developed by Li et al. [J. Comput. Phys., 170…

Numerical Analysis · Mathematics 2018-01-17 Hong Zhang , Paul A Zegeling

We consider the reliable implementation of high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their…

Numerical Analysis · Mathematics 2023-08-16 Zhiming Chen , Yong Liu

The thin plate spline smoother is a classical model for fnding a smooth function from the knowledge of its observation at scattered locations which may have random noises. We consider a nonconforming Morley finite element method to…

Numerical Analysis · Mathematics 2017-01-31 Zhiming Chen , Rui Tuo , Wenlong Zhang

We propose an adaptive polygonal finite element formulation for collapse plastic analysis of solids. The article contributes into four crucial points: 1) Wachspress shape functions at vertex and bubble nodes handled at a primal-mesh level;…

Computational Engineering, Finance, and Science · Computer Science 2016-06-30 H. Nguyen-Xuan , Son H. Nguyen , Hyun-Gyu Kim , Klaus Hackl

The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…

Numerical Analysis · Mathematics 2022-02-25 Qichen Hong , Hehu Xie , Fei Xu

Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property…

Mathematical Physics · Physics 2012-10-30 Larisa Beilina , Michael V. Klibanov

In this article, we introduce a finite element method designed for the robust computation of approximate signed distance functions to arbitrary boundaries in two and three dimensions. Our method employs a novel prediction-correction…

Computational Engineering, Finance, and Science · Computer Science 2025-06-24 Amina El Bachari , Johann Rannou , Vladislav A. Yastrebov , Pierre Kerfriden , Susanne Claus

This paper describes the use of the corotational cut Finite Element Method (FEM) for real-time surgical simulation. Users only need to provide a background mesh which is not necessarily conforming to the boundaries/interfaces of the…

Computational Engineering, Finance, and Science · Computer Science 2018-11-20 Huu Phuoc Bui , Satyendra Tomar , Stéphane P. A. Bordas

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

We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…

Numerical Analysis · Mathematics 2025-12-04 Amireh Mousavi

We study iterative finite element approximations for the numerical approximation of semilinear elliptic boundary value problems with monotone nonlinear reactions of subcritical growth. The focus of our contribution is on an optimal a priori…

Numerical Analysis · Mathematics 2025-08-18 Florian Spicher , Thomas P. Wihler

We address multiscale elliptic problems with random coefficients that are a perturbation of multiscale deterministic problems. Our approach consists in taking benefit of the perturbative context to suitably modify the classical Finite…

Numerical Analysis · Mathematics 2011-11-08 C. Le Bris , F. Legoll , F. Thomines

In this paper we study semi-discrete and fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation with a logarithmic potential. Specifically we consider linear finite elements discretising space and backward…

Numerical Analysis · Mathematics 2025-09-11 Charles M. Elliott , Thomas Sales

We develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together nicely in the sense that the intersection…

Numerical Analysis · Mathematics 2018-01-03 Peter Hansbo , Tobias Jonsson , Mats G. Larson , Karl Larsson

We design and analyze a new adaptive stabilized finite element method. We construct a discrete approximation of the solution in a continuous trial space by minimizing the residual measured in a dual norm of a discontinuous test space that…

Numerical Analysis · Mathematics 2020-04-22 Victor M. Calo , Alexandre Ern , Ignacio Muga , Sergio Rojas