Related papers: Finite element analysis for the Navier-Lam\'e eige…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…
We consider in this paper, a new a posteriori residual type error estimator of a conforming mixed finite element method for the coupling of fluid flow with porous media flow on isotropic meshes. Flows are governed by the Navier-Stokes and…
We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput.,…
We consider the approximation of elliptic eigenvalue problem with an immersed interface. The main aim of this paper is to prove the stability and convergence of an immersed finite element method (IFEM) for eigenvalues using Crouzeix-Raviart…
We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…
We study random eigenvalue problems in the context of spectral stochastic finite elements. In particular, given a parameter-dependent, symmetric positive-definite matrix operator, we explore the performance of algorithms for computing its…
In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear,…
A simple third order compact finite element method is proposed for one-dimensional Sturm-Liouville boundary value problems. The key idea is based on the interpolation error estimate, which can be related to the source term. Thus, a simple…
We consider the numerical computation of resonances for metallic grating structures with dispersive media and small slit holes. The underlying eigenvalue problem is nonlinear and the mathematical model is multiscale due to the existence of…
For the pure biharmonic equation and a biharmonic singular perturbation problem, a residual-based error estimator is introduced which applies to many existing nonconforming finite elements. The error estimator involves the local…
The paper deals with the a posteriori error analysis of a virtual element method for the Steklov eigenvalue problem. The virtual element method has the advantage of using general polygonal meshes, which allows implementing very efficiently…
In this paper we propose and analyze a virtual element method to approximate the natural frequencies of the acoustic eigenvalue problem with polygonal meshes that allow the presence of small edges. With the aid of a suitable seminorm that…
In this paper we consider the numerical approximation of the incompressible surface Navier--Stokes equations on an evolving surface. For the discrete representation of the moving surface we use parametric finite elements of degree $\ell…
We introduce novel a posteriori error indicators for a nonlinear least-squares solver for smooth solutions of the Monge--Amp\`ere equation on convex polygonal domains in $\mathbb{R}^2$. At each iteration, our iterative scheme decouples the…
The aim of this work is to analyze the finite element approximation of the two-dimensional stationary Navier-Stokes equations with non-smooth Dirichlet boundary data. The discrete approximation is obtained by considering the Navier-Stokes…
In this paper, we discuss approximating the eigenvalue problem of biharmonic equation. We first present an equivalent mixed formulation which admits amiable nested discretization. Then, we construct multi-level finite element schemes by…
We study the generalized finite element methods (GFEMs) for the second-order elliptic eigenvalue problem with an interface in 1D. The linear stable generalized finite element methods (SGFEM) were recently developed for the elliptic source…
This article is devoted to computing the lower and upper bounds of the Laplace eigenvalue problem. By using the special nonconforming finite elements, i.e., enriched Crouzeix-Raviart element and extension $Q_1^{\rm rot}$, we get the lower…
An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…