In this paper, we consider local and uniform invariance preserving steplength thresholds on a set when a discretization method is applied to a linear or nonlinear dynamical system. For the forward or backward Euler method, the existence of local and uniform invariance preserving steplength thresholds is proved when the invariant sets are polyhedra, ellipsoids, or Lorenz cones. Further, we also ...

Abstract. This paper deals with the formulation of a numerical scheme for solving compressible flow past moving bodies. We use the discontinuos Galerkin finite element method for the space semi-discretization and the Euler backward formula for the time discretization. Moreover, we use ALE mapping for the treatment of a time depended domain and the linearization of inviscid terms using the Vijay...

An error bound is proved for a fully practical piecewise linear nite element approximation, using a backward Euler time discretization, of the Cahn-Hilliard equation with a logarithmic free energy.

Abstract. Convergence of a full discretization is shown for a general class of nonlinear parabolic November 10, 2011 problems. The numerical method combines the backward Euler method for the time discretization with a generalized internal approximation scheme for the spatial discretization. The governing monotone elliptic differential operator is described by a nonlinearity that may have anisot...

This paper presents a sliding mode filter for removing noise. It effectively removes impulsive noise and high-frequency noise with producing smaller phase lag than linear filters. In addition, it is less prone to overshoot than previous sliding mode filters and it does not produce chattering. It is computationally inexpensive, and thus suitable for realtime applications. The proposed sliding mo...

The approximation of parabolic equations with nonhomogeneous Dirichlet boundary data by a numerical method that consists of finite elements for the space discretization and the backward Euler time discretization is studied. The boundary values are assumed in a least squares sense. It is shown that this method achieves an optimal rate of convergence for rough (only L1) boundary data and for smoo...

The numerical approximation to a parabolic control problem with control and state constraints is studied in this paper. We use standard piecewise linear and continuous finite elements for the space discretization of the state, while the backward Euler method is used for time discretization. A priori error estimates for control and state are obtained by an improved maximum error estimate for cor...

This paper is concerned with the time discretization of nonlinear evolution equations. We work in an abstract Banach space setting of analytic semigroups that covers fully nonlinear parabolic initial-boundary value problems with smooth coefficients. We prove convergence of variable stepsize backward Euler discretizations under various smoothness assumptions on the exact solution. We further sho...