Related papers: A lowest order mixed finite element method for the…
We consider mixed finite element methods for linear elasticity where the symmetry of the stress tensor is weakly enforced. Both an a priori and a posteriori error analysis are given for several known families of methods that are uniformly…
We establish an a priori error analysis for the lowest-order Raviart-Thomas finite element discretisation of the nonlinear Gross-Pitaevskii eigenvalue problem. Optimal convergence rates are obtained for the primal and dual variables as well…
As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…
The statistical behaviour of the smallest eigenvalue has important implications for systems which can be modeled using a Wishart-Laguerre ensemble, the regular one or the fixed trace one. For example, the density of the smallest eigenvalue…
The degree of entanglement of random pure states in bipartite quantum systems can be estimated from the distribution of the extreme Schmidt eigenvalues. For a bipartition of size M\geq N, these are distributed according to a…
A low-order nonconforming finite element discretization of a smooth de Rham complex starting from the $H^2$ space in three dimensions is proposed, involving an $H^2$-nonconforming finite element space, a new tangentially continuous…
We present new rectangular mixed finite elements for linear elasticity. The approach is based on a modification of the Hellinger-Reissner functional in which the symmetry of the stress field is enforced weakly through the introduction of a…
In this paper, we first discuss the optimal convergence of the adaptive finite element methods for non-self-adjoint eigenvalue problems. We present new theoretical error estimators and computable error estimators for multiple and clustered…
The purpose of this work is to study a finite element method for finding solutions to the eigenvalue problem for the fractional Laplacian. We prove that the discrete eigenvalue problem converges to the continuous one and we show the order…
In this work, we propose a mixed finite element method for solving elliptic multiscale problems based on a localized orthogonal decomposition (LOD) of Raviart-Thomas finite element spaces. It requires to solve local problems in small…
The transmission eigenvalue problem arising from the inverse scattering theory is of great importance in the theory of qualitative methods and in the practical applications. In this paper, we study the transmission eigenvalue problem for…
In this work, we fully explore three refined convergence structures of the lowest-order rectangular Raviart-Thomas element in solving the Laplace eigenvalue problem. Firstly, the scheme possesses a property of supercloseness between the…
This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly incompressible materials. The…
This work is motivated by the need to develop efficient tools for uncertainty quantification in subsurface flows associated with radioactive waste disposal studies. We consider single phase flow problems in random porous media described by…
This paper considers 3-D elastic scattering problems by penetrable obstacles with embedded objects. The well-posedness of transmission problem is proved by employing integral equation method. Then the Inverse Problems , which is to recover…
We give here a simplified presentation of the lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in three dimensions. The method can be applied to very general…
This paper studies adaptive least-squares finite element methods for convection-dominated diffusion-reaction problems. The least-squares methods are based on the first-order system of the primal and dual variables with various ways of…
We introduce and analyze a new mixed finite element method with reduced symmetry for the standard linear model in viscoelasticity. Following a previous approach employed for linear elastodynamics, the present problem is formulated as a…
The time discrete scheme of characteristics type is especially effective for convection-dominated diffusion problems. The scheme has been used in various engineering areas with different approximations in spatial direction. The lowest-order…
In this paper, we introduce and analyze a mixed formulation for the Oseen eigenvalue problem by introducing the pseudostress tensor as a new unknown, allowing us to eliminate the fluid pressure. The well-posedness of the solution operator…