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Time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run. In this paper, we derive theoretical convergence error estimates in discrete-time setting for…

Numerical Analysis · Mathematics 2020-03-04 Yerlan Amanbek , Mary Wheeler

We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected…

Numerical Analysis · Mathematics 2021-01-26 Erik Burman , Peter Hansbo , Mats G. Larson

This paper analyzes two eXtended finite element methods (XFEMs) for linear quadratic optimal control problems governed by Poisson equation in non-convex domains. We follow the variational discretization concept to discretize the continuous…

Numerical Analysis · Mathematics 2018-08-06 Tao Wang , Chao Chao Yang , Xiaoping Xie

We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics…

In this paper, we replace the asymptotic enrichments around the crack tip in the extended finite element method (XFEM) with the semi-analytical solution obtained by the scaled boundary finite element method (SBFEM). The proposed method does…

Numerical Analysis · Mathematics 2013-09-04 Sundararajan Natarajan , Chongmin Song

This paper is devoted to the construction and analysis of immersed finite element (IFE) methods in three dimensions. Different from the 2D case, the points of intersection of the interface and the edges of a tetrahedron are usually not…

Numerical Analysis · Mathematics 2023-02-03 Haifeng Ji

The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the…

Computational Physics · Physics 2012-02-20 J. E. Sprittles , Y. D. Shikhmurzaev

We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite Element Method. The latter method is a now classical, finite…

Numerical Analysis · Mathematics 2024-11-12 Rutger A. Biezemans , Claude Le Bris , Frédéric Legoll , Alexei Lozinski

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…

Numerical Analysis · Mathematics 2015-08-11 Donald L. Brown , Maria Vasilyeva

A brief summary of direct solution approaches for finite element methods (FEM) in computational electromagnetics (CEM) is given along with an alternative direct solution based on domain decomposition (DD). Unlike recent trends in…

Computational Engineering, Finance, and Science · Computer Science 2020-02-13 Javad Moshfegh , Marinos N. Vouvakis

Fast and high-order accurate algorithms for three dimensional elastic scattering are of great importance when modeling physical phenomena in mechanics, seismic imaging, and many other fields of applied science. In this paper, we develop a…

Numerical Analysis · Mathematics 2021-04-09 Jun Lai , Heping Dong

Finite element methods for electromagnetic problems modeled by Maxwell-type equations are highly sensitive to the conformity of approximation spaces, and non-conforming methods may cause loss of convergence. This fact leads to an essential…

Numerical Analysis · Mathematics 2023-04-05 Shuhao Cao , Long Chen , Ruchi Guo

In this paper, we introduce the locally conservative enriched immersed finite element method (EIFEM) to tackle the elliptic problem with interface. The immersed finite element is useful for handling interface with mesh unfit with the…

Numerical Analysis · Mathematics 2021-01-05 Gwanghyun Jo , Do Young Kwak , Young Ju Lee

We review the main features of an unfitted finite element method for interface and fluid-structure interaction problems based on a distributed Lagrange multiplier in the spirit of the fictitious domain approach. We recall our theoretical…

Numerical Analysis · Mathematics 2025-10-03 Najwa Alshehri , Daniele Boffi , Fabio Credali , Lucia Gastaldi

We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a…

Numerical Analysis · Mathematics 2015-11-10 Erik Burman , Peter Hansbo , Mats G. Larson , Sara Zahedi

In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…

Computational Physics · Physics 2026-02-18 F. Şık , F. L. Teixeira , B. Shanker

Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion…

Numerical Analysis · Mathematics 2015-01-20 Andrea Bonito , Ronald A. DeVore , Ricardo H. Nochetto

Guaranteed upper-lower bounds on homogenized coefficients, arising from the periodic cell problem, are calculated in a scalar elliptic setting. Our approach builds on the recent variational reformulation of the Moulinec-Suquet (1994) Fast…

Numerical Analysis · Computer Science 2015-11-06 Jaroslav Vondřejc , Jan Zeman , Ivo Marek

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

The Fourier-Galerkin method (in short FFTH) has gained popularity in numerical homogenisation because it can treat problems with a huge number of degrees of freedom. Because the method incorporates the fast Fourier transform (FFT) in the…

Numerical Analysis · Mathematics 2020-02-14 Jaroslav Vondřejc , Tom W. J. de Geus