Related papers: Higher order stable generalized finite element met…
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…
We establish robust exponential convergence for $rp$-Finite Element Methods (FEMs) applied to fourth order singularly perturbed boundary value problems, in a \emph{balanced norm} which is stronger than the usual energy norm associated with…
A stabilizing/penalty term is often used in finite element methods with discontinuous approximations to enforce connection of discontinuous functions across element boundaries. Removing stabilizers from discontinuous finite element methods…
A new immersed finite element (IFE) method is developed for second-order elliptic problems with discontinuous diffusion coefficient. The IFE space is constructed based on the rotated Q1 nonconforming finite elements with the integral-value…
We propose a new nonconforming \(P_1\) finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of…
This article is devoted to computing the eigenvalue of the Laplace eigenvalue problem by the weak Galerkin (WG) finite element method with emphasis on obtaining lower bounds. The WG method is on the use of weak functions and their weak…
We propose and analyze novel adaptive algorithms for the numerical solution of elliptic partial differential equations with parametric uncertainty. Four different marking strategies are employed for refinement of stochastic Galerkin finite…
We present the numerical analysis of a finite element method (FEM) for one-dimensional Dirichlet problems involving the logarithmic Laplacian (the pseudo-differential operator that appears as a first-order expansion of the fractional…
High-order discontinuous Galerkin spectral element methods (DGSEM) have received growing attention and development, especially in the regime of computational fluid dynamics in recent years. The inherent flexibility of the discontinuous…
This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial…
In this paper, we propose an extended mixed finite element method for elliptic interface problems. By adding some stabilization terms, we present a mixed approximation form based on Brezzi-Douglas-Marini element space and the piecewise…
In this paper, we propose oversampling strategies in the Generalized Multiscale Finite Element Method (GMsFEM) framework. The GMsFEM, which has been recently introduced in [12], allows solving multiscale parameter-dependent problems at a…
We present a novel, high-order, efficient, and exponentially convergent shifted Gegenbauer integral pseudospectral method (SGIPSM) to solve numerically Lane-Emden equations provided with some mixed Neumann and Robin boundary conditions. The…
We study some numerical methods for solving second order elliptic problem with interface. We introduce an immersed interface finite element method based on the `broken' $P_1$-nonconforming piecewise linear polynomials on interface…
Numerical homogenization and multiscale finite element methods construct effective properties on a coarse grid by solving local problems and extracting the average effective properties from these local solutions. In some cases, the…
Maxwell interface problems are of great importance in many electromagnetic applications. Unfitted mesh methods are especially attractive in 3D computation as they can circumvent generating complex 3D interface-fitted meshes. However, many…
The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which…
In this paper, we propose a linearized finite element method (FEM) for solving the cubic nonlinear Schr\"{o}dinger equation with wave operator. In this method, a modified leap-frog scheme is applied for time discretization and a Galerkin…
A hybrid computational approach that integrates the finite element method (FEM) with least squares support vector regression (LSSVR) is introduced to solve partial differential equations. The method combines FEM's ability to provide the…
This article concerns the weak Galerkin mixed finite element method (WG-MFEM) for second order elliptic equations on 2D domains with curved boundary. The Neumann boundary condition is considered since it becomes the essential boundary…