English
Related papers

Related papers: An energy-stable parametric finite element method …

200 papers

Achieving accurate numerical results of hydrodynamic loads based on the potential-flow theory is very challenging for structures with sharp edges, due to the singular behavior of the local-flow velocities. In this paper, we introduce the…

Numerical Analysis · Mathematics 2021-09-23 Ying Wang , Yanlin Shao , Jikang Chen , Hui Liang

Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…

Numerical Analysis · Mathematics 2024-09-04 Ahmad Deeb , Denys Dutykh

This work presents a polyhedral scaled boundary finite element method (PSBFEM) for three dimensional seepage analysis. We first derive the scaled boundary formulation for 3D seepage problems, and subsequently incorporate Wachspress shape…

Numerical Analysis · Mathematics 2025-06-11 Mingjiao Yan , Yang Yang , Zongliang Zhang , Dengmiao Hao , Chao Su , Qingsong Duan

In this paper we propose a method for the construction of locally conservative flux fields from Generalized Multiscale Finite Element Method (GMsFEM) pressure solutions. The flux values are obtained from an element-based postprocessing…

Analysis of PDEs · Mathematics 2013-04-24 Lawrence Bush , Victor Ginting , Michael Presho

We consider a Stokes problem posed on a 2D surface embedded in a 3D domain. The equations describe an equilibrium, area-preserving tangential flow of a viscous surface fluid and serve as a model problem in the dynamics of material…

Numerical Analysis · Mathematics 2018-01-23 Maxim A. Olshanskii , Annalisa Quaini , Arnold Reusken , Vladimir Yushutin

Deformable elastic bodies in viscous and viscoelastic media constitute a large portion of synthetic and biological complex fluids. We present a parallelized 3D-simulation methodology which fully resolves the momentum balance in the solid…

Computational Physics · Physics 2019-03-11 Amir Saadat , Chris J. Guido , Gianluca Iaccarino , Eric S. G. Shaqfeh

We propose a new unfitted finite element method for simulation of two-phase flows in presence of insoluble surfactant. The key features of the method are 1) discrete conservation of surfactant mass; 2) the possibility of having meshes that…

Numerical Analysis · Mathematics 2022-11-30 Thomas Frachon , Sara Zahedi

We propose new formulations of geometric curvature flows -- referred to as \emph{dual formulations} -- that are equivalent to the original formulations but provide a novel framework for constructing linearly implicit and energy-stable…

Numerical Analysis · Mathematics 2026-04-28 Guangwei Gao , Buyang Li , Rong Tang

A new finite element method (FEM) using meshes that do not necessarily align with the interface is developed for two- and three-dimensional anisotropic elliptic interface problems with nonhomogeneous jump conditions. The degrees of freedom…

Numerical Analysis · Mathematics 2025-05-20 Haifeng Ji , Zhilin Li

The scaled boundary finite element method (SBFEM) is a semi-analytical computational scheme, which is based on the characteristics of the finite element method (FEM) and combines the advantages of the boundary element method (BEM). This…

Numerical Analysis · Mathematics 2024-10-22 Yang Yang , Zongliang Zhang , Yelin Feng

In this work we present a novel monolithic Finite Element Method (FEM) for the hydroelastic analysis of Very Large Floating Structures (VLFS) with arbitrary shapes that is stable, energy conserving and overcomes the need of an iterative…

Computational Engineering, Finance, and Science · Computer Science 2022-06-28 Oriol Colomés , Francesc Verdugo , Ido Akkerman

Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse a fully discrete numerical method of this geometric evolution equation. The method uses piecewise linear finite elements in space and a backward…

Numerical Analysis · Mathematics 2023-03-01 Klaus Deckelnick , Robert Nürnberg

Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…

Computational Engineering, Finance, and Science · Computer Science 2019-02-05 Bilen Emek Abali

In this paper, we consider mixed finite element semi-/full discretizations of the Rosensweig ferrofluid flow model. We first establish some regularity results for the model under several basic assumptions. Then we show that the energy…

Numerical Analysis · Mathematics 2024-12-03 Yongke Wu , Xiaoping Xie

This work concerns the numerical approximation of a multicomponent compressible Euler system for a fluid mixture in multiple space dimensions on unstructured meshes with a high-order discontinuous Galerkin spectral element method (DGSEM).…

Numerical Analysis · Mathematics 2021-08-25 Florent Renac

This paper introduces a family of entropy-conserving finite-difference discretizations for the compressible flow equations. In addition to conserving the primary quantities of mass, momentum, and total energy, the methods also preserve…

Fluid Dynamics · Physics 2025-09-24 Carlo De Michele , Ayaboe K. Edoh , Gennaro Coppola

Many problems in electrical engineering or fluid mechanics can be modeled by parabolic-elliptic interface problems, where the domain for the exterior elliptic problem might be unbounded. A possibility to solve this class of problems…

Numerical Analysis · Mathematics 2018-05-15 Christoph Erath , Robert Schorr

In this work, we present the construction of two distinct finite element approaches to solve the Porous Medium Equation (PME). In the first approach, we transform the PME to a log-density variable formulation and construct a continuous…

Numerical Analysis · Mathematics 2023-03-28 Arjun Vijaywargiya , Guosheng Fu

In this paper, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of…

Numerical Analysis · Mathematics 2025-10-23 Ruben Caraballo , Chansophea Wathanak In , Alberto F. Martín , Ricardo Ruiz-Baier

Persistent homology is a relatively new tool often used for \emph{qualitative} analysis of intrinsic topological features in images and data originated from scientific and engineering applications. In this paper, we report novel…

Biomolecules · Quantitative Biology 2014-12-09 Kelin Xia , Xin Feng , Yiying Tong , Guo Wei We