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This paper introduces a new weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This method, called WG-FEM, is designed by using a discrete weak gradient operator applied to discontinuous…

Numerical Analysis · Mathematics 2012-08-20 Lin Mu , Junping Wang , Xiu Ye

Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…

Fluid Dynamics · Physics 2025-12-24 Thomas Leyssens , Jonathan Lambrechts , Jean-François Remacle

In this paper we analyze the error as well for the semi-discretization as the full discretization of a time-dependent convection-diffusion problem. We use for the discretization in space the local discontinuous Galerkin (LDG) method on a…

Numerical Analysis · Mathematics 2020-12-08 Yao Cheng , Yanjie Mei , Hans-Goerg Roos

This article initiates the study of space-time adaptive mesh refinements for time-dependent boundary element formulations of wave equations. Based on error indicators of residual type, we formulate an adaptive boundary element procedure for…

Numerical Analysis · Mathematics 2025-11-07 Alessandra Aimi , Giulia Di Credico , Heiko Gimperlein , Chiara Guardasoni

This study presents an adaptive coupling peridynamic least-square minimization with the finite element method (PDLSM-FEM) for fracture analysis. The presented method utilizes the PDLSM modeling discontinuities while maximizing the FEM…

Numerical Analysis · Mathematics 2022-06-22 Qibang Liu , X. J. Xin , Jeff Ma

In this work is considered a spectral problem, involving a second order term on the domain boundary: the Laplace-Beltrami operator. A variational formulation is presented, leading to a finite element discretization. For the Laplace-Beltrami…

Numerical Analysis · Mathematics 2024-04-23 Fabien Caubet , Joyce Ghantous , Charles Pierre

We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…

Numerical Analysis · Mathematics 2020-06-08 Quan Zhao , Wei Jiang , Weizhu Bao

We propose consistent locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of non-autonomous parabolic evolution problems under the assumption of maximal…

Numerical Analysis · Mathematics 2019-03-07 Ulrich Langer , Andreas Schafelner

An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…

Numerical Analysis · Mathematics 2018-06-27 Jorgen S. Dokken , Simon W. Funke , August Johansson , Stephan Schmidt

Shape-morphing solutions (SMS) refer to a class of approximate solutions of partial differential equations (PDEs) with the distinguishing feature that they depend nonlinearly on a set of time-dependent parameters. They generalize Galerkin…

Numerical Analysis · Mathematics 2026-03-23 Mohammad Farazmand

This paper presents a new methodology for structural reliability analysis via stochastic finite element method (SFEM). A novel sample-based SFEM is firstly used to compute structural stochastic responses of all spatial points at the same…

Computational Physics · Physics 2020-08-19 Zhibao Zheng

We consider goal-oriented adaptive space-time finite-element discretizations of the regularized parabolic p-Laplace problem on completely unstructured simplicial space-time meshes. The adaptivity is driven by the dual-weighted residual…

Numerical Analysis · Mathematics 2023-06-13 B. Endtmayer , U. Langer , A. Schafelner

We present a new time-stepping criterion for N-body simulations that is based on the true dynamical time of a particle. This allows us to follow the orbits of particles correctly in all environments since it has better adaptivity than…

Astrophysics · Physics 2009-10-12 Marcel Zemp , Joachim Stadel , Ben Moore , C. Marcella Carollo

This work presents the Griffith-type phase-field formation at large deformation in the framework of adaptive edge-based smoothed finite element method (ES-FEM) for the first time. Therein the phase-field modeling of fractures has attracted…

Numerical Analysis · Mathematics 2021-11-09 Fucheng Tian , Xiaoliang Tang , Tingyu Xu , Liangbin Li

This paper focuses on identifying the cause and proposing a remedy for the problem of spurious pressure oscillations in a sharp-interface immersed boundary finite element method for incompressible flow problems in moving domains. The…

Numerical Analysis · Mathematics 2025-10-14 Maxim Olshanskii , Henry von Wahl

We consider the well-posedness and a priori error estimates of a 3d FEM-BEM coupling method for fluid-structure interaction in the time domain. For an elastic body immersed in a fluid, the exterior linear wave equation for the fluid is…

Numerical Analysis · Mathematics 2020-08-12 Heiko Gimperlein , Ceyhun Oezdemir , Ernst P. Stephan

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…

Numerical Analysis · Mathematics 2023-07-19 Alexey Y. Chernyshenko , Maxim A. Olshanskii

A semidiscrete Galerkin finite element method applied to time-fractional diffusion equations with time-space dependent diffusivity on bounded convex spatial domains will be studied. The main focus is on achieving optimal error results with…

Numerical Analysis · Mathematics 2020-06-12 Kassem Mustapha

Adaptivity and local mesh refinement are crucial for the efficient numerical simulation of wave phenomena in complex geometry. Local mesh refinement, however, can impose a tiny time-step across the entire computational domain when using…

Numerical Analysis · Mathematics 2024-09-27 Marcus J. Grote , Simon R. J. Michel , Stefan A. Sauter

We consider the damped time-harmonic Galbrun's equation, which is used to model stellar oscillations. We introduce a discontinuous Galerkin finite element method (DGFEM) with $H(\operatorname{div})$-elements, which is nonconform with…

Numerical Analysis · Mathematics 2023-06-07 Martin Halla