An analysis of the convergence of mixed finite element methods
An analysis of the effect of ghost force oscillation on quasicontinuum error
The atomistic to continuum interface for quasicontinuum energies exhibits nonzero forces under uniform strain that have been called ghost forces. In this paper, we prove for a linearization of a one-dimensional quasicontinuum energy around a uniform strain that the effect of the ghost forces on the displacement nearly cancels and has a small effect on the error away from the interface. We give optimal order error estimates that show that the quasicontinuum displacement converges to the atomistic...
An analysis of the influence of data extrema on some first and second order central approximations of hyperbolic conservation laws
We discuss the occurrence of oscillations when using central schemes of the Lax-Friedrichs type (LFt), Rusanov’s method and the staggered and non-staggered second order Nessyahu-Tadmor (NT) schemes. Although these schemes are monotone or TVD, respectively, oscillations may be introduced at local data extrema. The dependence of oscillatory properties on the numerical viscosity coefficient is investigated rigorously for the LFt schemes, illuminating also the properties of Rusanov’s method. It turns...
An analysis of the influence of data extrema on some first and second order central approximations of hyperbolic conservation laws
We discuss the occurrence of oscillations when using central schemes of the Lax-Friedrichs type (LFt), Rusanov's method and the staggered and non-staggered second order Nessyahu-Tadmor (NT) schemes. Although these schemes are monotone or TVD, respectively, oscillations may be introduced at local data extrema. The dependence of oscillatory properties on the numerical viscosity coefficient is investigated rigorously for the LFt schemes, illuminating also the properties of Rusanov's method. It turns...
An Analysis of the Numerical Solution of Fredholm Integral Equations of the First Kind.
An analysis of the pole placement problem I: The single-input case.
An analysis of the pole placement problem. II: The multi-input case.
An Analysis of the p-Version of the Finite Element Method for Nearly Incompressible Materials. Uniformly Valid, Optimal Error Estimates
An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations
An Analysis of the Shifted LR Algorithm.
An analysis technique for stabilized finite element solution of incompressible flows
This paper presents an extension to stabilized methods of the standard technique for the numerical analysis of mixed methods. We prove that the stability of stabilized methods follows from an underlying discrete inf-sup condition, plus a uniform separation property between bubble and velocity finite element spaces. We apply the technique introduced to prove the stability of stabilized spectral element methods so as stabilized solution of the primitive equations of the ocean.
An analysis technique for stabilized finite element solution of incompressible flows
This paper presents an extension to stabilized methods of the standard technique for the numerical analysis of mixed methods. We prove that the stability of stabilized methods follows from an underlying discrete inf-sup condition, plus a uniform separation property between bubble and velocity finite element spaces. We apply the technique introduced to prove the sta bi li ty of stabilized spectral element methods so as stabilized solution of the primitive equations of the ocean.
An analytic proof of numerical stability of Gaussian collocation for delay differential
In questo articolo si investigano le proprietà di stabilità asintotica dei metodi numerici per equazioni differenziali con ritardo, prendendo in esame l'equazione test: dove , , e è una funzione a valori reali e continua. In particolare, viene analizzata la dipendenza dal ritardo della stabilità numerica dei metodi di collocazione Gaussiana. Nel recente lavoro [GH99], la stabilità di questi metodi è stata dimostrata facendo uso di un approccio geometrico, basato sul legame tra la proprietà...
An analytical and numerical approach to a bilateral contact problem with nonmonotone friction
We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach...
An analytical approach for quasi-linear equation in second order.
An analytical method for calculation of integrals appearing in approximate solutions of deformable body mechanics
An application of semi-infinite linear programming: approximation of a continuous function by a polynomial
An application of the averaged gradient technique
An application of the BDDC method to the Navier-Stokes equations in 3-D cavity
We deal with numerical simulation of incompressible flow governed by the Navier-Stokes equations. The problem is discretised using the finite element method, and the arising system of nonlinear equations is solved by Picard iteration. We explore the applicability of the Balancing Domain Decomposition by Constraints (BDDC) method to nonsymmetric problems arising from such linearisation. One step of BDDC is applied as the preconditioner for the stabilized variant of the biconjugate gradient (BiCGstab)...
An application of the finite element method for solving the system of partial differential equations