Related papers: Finite Element Approximation of a Strain-Limiting …
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 propose a nonconforming finite element method for the solution of the ill-posed elliptic Cauchy problem. We prove error estimates using continuous dependence estimates in the $L^2$-norm. The effect of perturbations in data…
In this paper we discuss the adjoint stabilised finite element method introduced in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problems. Part I: elliptic equations, SIAM Journal on Scientific…
Unfitted finite element techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to severe ill conditioning problems that obstruct the efficient use…
For calculating large deformations in finite elasticity, we have proposed a method of successive linear approximation, by considering the relative descriptional formulation. In this article we briefly describe this method and we prove the…
We study a fully discrete finite element approximation of a model for unsteady flows of rate-type viscoelastic fluids with stress diffusion in two and three dimensions. The model consists of the incompressible Navier--Stokes equation for…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
We develop a fully discrete, semi-implicit mixed finite element method for approximating solutions to a class of fourth-order stochastic partial differential equations (SPDEs) with non-globally Lipschitz and non-monotone nonlinearities,…
The thin plate spline smoother is a classical model for fnding a smooth function from the knowledge of its observation at scattered locations which may have random noises. We consider a nonconforming Morley finite element method to…
A family of mixed finite elements is proposed for solving the first order system of linear elasticity equations in any space dimension, where the stress field is approximated by symmetric finite element tensors. This family of elements has…
Consider the scattering of an elastic plane wave by a rigid obstacle, which is immersed in a homogeneous and isotropic elastic medium in two dimensions. Based on a Dirichlet-to-Neumann (DtN) operator, an exact transparent boundary condition…
A stress equilibration procedure for linear elasticity is proposed and analyzed in this paper with emphasis on the behavior for (nearly) incompressible materials. Based on the displacement-pressure approximation computed with a stable…
We consider a unique continuation problem where the Dirichlet trace of the solution is known to have finite dimension. We prove Lipschitz stability of the unique continuation problem and design a finite element method that exploits the…
We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…
We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove convergence of an…
This paper proposes and analyzes a class of new weak Galerkin (WG) finite element methods for 2- and 3-dimensional linear elasticity problems. The methods use discontinuous piecewise-polynomial approximations of degrees $k(\geq 0)$ for the…
We present an efficient and robust numerical algorithm for solving the two-dimensional linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve…
In this study we establish the existence and uniqueness of the solution of a coupled system of general elliptic equations with anisotropic diffusion , non-uniform advection and variably influencing reaction terms on Lipschitz continuous…
We use inverted finite elements method for approximating solutions of second order elliptic equations with non-constant coefficients varying to infinity in the exterior of a 2D bounded obstacle, when a Neumann boundary condition is…
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…