Related papers: Stable Generalized Finite Element Method (SGFEM)
We describe a new finite element method (FEM) to construct continuous equilibrium distribution functions of stellar systems. The method is a generalization of Schwarzschild's orbit superposition method from the space of discrete functions…
We consider the construction of the stochastic moment matrices that appear in the typical elliptic diffusion problem considered in the setting of stochastic Galerkin finite element method (sGFEM). Algorithms for the efficient construction…
In this work, we propose a generalized multiscale inversion algorithm for heterogeneous problems that aims at solving an inverse problem on a computational coarse grid. Previous inversion techniques for multiscale problems seek a…
The scaled boundary finite element method (SBFEM) has recently been employed as an efficient means to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
Despite the increasing use of the Particle Finite Element Method (PFEM) in fluid flow simulation and the outstanding success of the Generalized-alpha time integration method, very little discussion has been devoted to their combined…
We propose and analyze a unified structure-preserving parametric finite element method (SP-PFEM) for the anisotropic surface diffusion of curves in two dimensions $(d=2)$ and surfaces in three dimensions $(d=3)$ with an arbitrary…
Many problems in physics are inherently of multi-scale nature. The issues of MHD turbulence or magnetic reconnection, namely in the hot and sparse, almost collision-less astrophysical plasmas, can stand as clear examples. The Finite Element…
The intrusive (sample-free) spectral stochastic finite element method (SSFEM) is a powerful numerical tool for solving stochastic partial differential equations (PDEs). However, it is not widely adopted in academic and industrial…
We present the first rigorous convergence analysis of the smoothed adaptive finite element method (S-AFEM) proposed in [Mulita, Giani, Heltai: SIAM J. Sci. Comput. 43, 2021]. S-AFEM modifies the classical adaptive finite element method…
In this paper, we consider the numerical solution of poroelasticity problems that are of Biot type and develop a general algorithm for solving coupled systems. We discuss the challenges associated with mechanics and flow problems in…
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…
This work develops novel energy-stable parametric finite element methods (ES-PFEM) for the Willmore flow and curvature-dependent geometric gradient flows of surfaces in three dimensions. The key to achieving the energy stability lies in the…
This paper presents the first time implementation of the eXtended Finite Element Method (XFEM) in the general purpose commercial software COMSOL Multiphysics. An enrichment strategy is proposed, consistent with the structure of the…
This paper focuses on the study of the Filament Based Lamellipodium Model (FBLM) and the corresponding Finite Element Method (FEM) from a numerical point of view. We study fundamental numerical properties of the FEM and justify the further…
Finite element method (FEM) is one of the most important numerical methods in modern engineering design and analysis. Since traditional serial FEM is difficult to solve large FE problems efficiently and accurately, high-performance parallel…
We present a machine-learning strategy for finite element analysis of solid mechanics wherein we replace complex portions of a computational domain with a data-driven surrogate. In the proposed strategy, we decompose a computational domain…
In this paper, we study the development of efficient multiscale methods for flows in heterogeneous media. Our approach uses the Generalized Multiscale Finite Element (GMsFEM) framework. The main idea of GMsFEM is to approximate the solution…
Multiscale Finite Element Methods (MsFEM) are finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions which generate a specific discretization space, and next…
The Heterogeneous Multiscale Finite Element Method (FE-HMM) is a two-scale FEM based on asymptotic homogenization for solving multiscale partial differential equations. It was introduced in [W. E and B. Engquist, \emph{Commun. Math. Sci.},…