Related papers: Nitsche's method for Kirchhoff plates
We prove a three sphere inequality with optimal exponent at the boundary for solutions to the Kirchhoff-Love plate's equation satisfying homogeneous Dirichlet conditions. This result implies the Strong Unique Continuation Property at the…
Exact boundary conditions at finite distance for the solutions of the time-dependent Schrodinger equation are derived. A numerical scheme based on Crank-Nicholson method is proposed to illustrate its applicability in several examples.
A set of curved beams and shells is geometrically implied by level sets of a scalar function over some bulk domain. The mechanical model for each structure is based on the Kirchhoff--Love theory, that is, small displacements without shear…
We formulate and analyze a Nitsche-type algorithm for frictional contact problems. The method is derived from, and analyzed as, a stabilized finite element method and shown to be quasi-optimal, as well as suitable as an adaptive scheme…
We completely characterize Birkhoff-James orthogonality with respect to numerical radius norm in the space of bounded linear operators on a complex Hilbert space. As applications of the results obtained, we estimate lower bounds of…
In this article we give a brief overview of some known results in the theory of obstacle-type problems associated with a class of fourth-order elliptic operators, and we highlight our recent work with collaborators in this direction.…
We address the problem of bounding rigorously the errors in the numerical solution of the Kohn-Sham equations due to (i) the finiteness of the basis set, (ii) the convergence thresholds in iterative procedures, (iii) the propagation of…
We study the inverse problem of determining the Winkler coefficient in a nanoplate resting on an elastic foundation and clamped at the boundary. The nanoplate is described within a simplified strain gradient elasticity theory for isotropic…
We deal with the existence of weak solutions for a mixed Neumann-Robin-Cauchy problem. The existence results are based on global-in-time estimates of approximating solutions, and the passage to the limit exploits compactness techniques. We…
We consider a time-dependent coupled Navier--Stokes/generalized poroelastic flow problem and propose a unified and monolithic finite element discretization based on implicit time stepping. To handle the fluid-structure interface we employ a…
In this paper, we study the stability of the nonsymmetric version of Nitsche's method without penalty for compressible and incompressible elasticity. For the compressible case we prove the convergence of the error in the $H^1$- and…
The aim of this work is to study the numerical solution of the nonlinear Schrodinger problem using a combination between Witt basis and finite difference approximations. We construct a discrete fundamental solution for the non-stationary…
We propose a Nitsche-based fictitious domain method for the three field Stokes problem in which the boundary of the domain is allowed to cross through the elements of a fixed background mesh. The dependent variables of velocity, pressure…
Multivariate Poisson approximation of the length spectrum of random surfaces is studied by means of the Chen-Stein method. This approach delivers simple and explicit error bounds in Poisson limit theorems. They are used to prove that…
The purpose of this work is to study an approximation to an abstract Bessel-type problem, which is a generalization of the extension problem associated with fractional powers of the Laplace operator. Motivated by the success of such…
We present two simple finite element methods for the discretization of Reissner--Mindlin plate equations with {\em clamped} boundary condition. These finite element methods are based on discrete Lagrange multiplier spaces from mortar finite…
In this paper we demonstrate for the first time that it is possible to solve numerically the Cauchy problem for the linearisation of the general conformal field equations near spacelike infinity, which is only well-defined in Friedrich's…
We present and analyze an a posteriori error estimator based on mesh refinement for the solution of the hypersingular boundary integral equation governing the Laplacian in three dimensions. The discretization under consideration is a…
In this paper we consider a generalized fourth order nonlinear Kirchhoff equation in a bounded domain in $\mathbb R^{N}, N\geq2$ under Navier boundary conditions and with sublinear nonlinearity. We employ a change of variable which reduces…
We propose a new splitting method for strong numerical solution of the Cox-Ingersoll-Ross model. For this method, applied over both deterministic and adaptive random meshes, we prove a uniform moment bound and strong error results of order…