Related papers: Linear smoothed extended finite element method
Current Event Stream Super-Resolution (ESR) methods overlook the redundant and complementary information present in positive and negative events within the event stream, employing a direct mixing approach for super-resolution, which may…
We develop a discontinuous cut finite element method (CutFEM) for the Laplace-Beltrami operator on a hypersurface embedded in $\mathbb{R}^d$. The method is constructed by using a discontinuous piecewise linear finite element space defined…
Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales (see Figure 1 for the illustration of a perforated domain).…
We propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages. In the…
In this paper, we examine the effectiveness of classic multiscale finite element method (MsFEM) (Hou and Wu, 1997; Hou et al., 1999) for mixed Dirichlet-Neumann, Robin and hemivariational inequality boundary problems. Constructing so-called…
In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the…
We present a multiscale mixed finite element method for solving second order elliptic equations with general $L^{\infty}$-coefficients arising from flow in highly heterogeneous porous media. Our approach is based on a multiscale spectral…
We propose a novel efficient and robust Wavelet-based Edge Multiscale Finite Element Method (WEMsFEM) motivated by \cite{MR3980476,GL18} to solve the singularly perturbed convection-diffusion equations. The main idea is to first establish a…
In this paper we analyze a space-time unfitted finite element method for the discretization of scalar surface partial differential equations on evolving surfaces. For higher order approximations of the evolving surface we use the technique…
The Generalized Finite Element Method (GFEM) is an effective unfitted numerical method for handling interface problems. By augmenting the standard FEM space with an appropriate enrichment space, GFEM can accurately capture C^0 solutions…
In this paper, for the generalized Darcy problem (an elliptic equation with discontinuous coefficients), we study a special partial Least-Squares (Galerkin-least-squares) method, known as the augmented mixed finite element method, and its…
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…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
Finite element method (FEM) suffers from a serious mesh distortion problem when used for high velocity impact analyses. The smooth particle hydrodynamics (SPH) method is appropriate for this class of problems involving severe damages but at…
In this article we study adaptive finite element methods (AFEM) with inexact solvers for a class of semilinear elliptic interface problems. We are particularly interested in nonlinear problems with discontinuous diffusion coefficients, such…
In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of…
Periodic micromagnetic finite element method (PM-FEM) is introduced to solve periodic unit cell problems using the Landau-Lifshitz-Gilbert equation. PM-FEM is applicable to general problems with 1D, 2D, and 3D periodicities. PM-FEM is based…
The combination of Finite Element Method (FEM) simulation and experimental photo-elasticity provides both qualitative and quantitative information about the stress field in a polymer composite and particularly along the fibre-matrix…
Cut finite element method (CutFEM) based approaches towards challenging fluid-structure interaction (FSI) are proposed. The different considered methods combine the advantages of competing novel Eulerian (fixed-grid) and established…
We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…