Related papers: A variational approach to high-order r-adaptation

We consider the vertex-centered finite volume method with first-order conforming ansatz functions. The adaptive mesh-refinement is driven by the local contributions of the weighted-residual error estimator. We prove that the adaptive…

We propose a simple and efficient scheme based on adaptive finite elements over conforming quadtree meshes for collapse plastic analysis of structures. Our main interest in kinematic limit analysis is concerned with both purely…

In this paper we propose a high-order accurate scheme for image segmentation based on the level-set method. In this approach, the curve evolution is described as the 0-level set of a representation function but we modify the velocity that…

First-order operator splitting methods are ubiquitous among many fields through science and engineering, such as inverse problems, signal/image processing, statistics, data science and machine learning, to name a few. In this paper, we…

We study adaptive mesh selection for the solution of systems of initial value problems. The goal is a rigorous theoretical analysis of potential advantages of adaption. For an optimal method in the sense of the speed of convergence, we…

The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk…

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…

This work proposes an adaptive framework to solve a robust structural shape optimization problem governed by linear elasticity models that account for uncertainties in the loading and material inputs. A posteriori error estimators are…

An adaptive moving mesh finite element method is studied for the numerical solution of the porous medium equation with and without variable exponents and absorption. The method is based on the so-called moving mesh partial differential…

A mesh improvement methodology is pre- sented which aims to improve the quality of the worst elements in 3D meshes with non-planar surfaces which cannot be improved using traditional methods. A nu- merical optimisation algorithm, which…

The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…

This article discusses a mixed FE technique for 3D nonlinear elasticity using a Hu-Washizu (HW) type variational principle. Here, the deformed configuration and sections from its cotangent bundle are taken as additional input arguments. The…

We introduce a hyperreduced reduced basis element method for model reduction of parameterized, component-based systems in continuum mechanics governed by nonlinear partial differential equations. In the offline phase, the method constructs,…

We present an online-adaptive hyperreduced reduced basis element method for model order reduction of parameterized, component-based nonlinear systems. The method, in the offline phase, prepares a library of hyperreduced archetype components…

This contribution introduces the idea of refinement patterns for the generation of optimal meshes in the context of the Finite Element Method. The main idea is to generate a library of possible patterns on which elements can be refined and…

In this paper, we propose the MultiLevel Variational MultiScale (ML-VMS) method, a novel approach that seamlessly integrates a multilevel mesh strategy into the Variational Multiscale (VMS) framework. A key feature of the ML-VMS method is…

Parameter-efficient fine-tuning for pre-trained Vision Transformers aims to adeptly tailor a model to downstream tasks by learning a minimal set of new adaptation parameters while preserving the frozen majority of pre-trained parameters.…

This paper presents a computational framework for the robust stiffness design of hyperelastic structures at finite deformations subject to various uncertain sources. In particular, the loading, material properties, and geometry…

We apply an unfitted HDG discretization to a model problem in shape optimization. The method proposed uses a fixed, shape regular, non-geometry conforming mesh and a high order transfer technique to deal with the curved boundaries arising…

In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…