Abstract. We present an analysis for a mixed finite element method for the bending problem of Koiter shell. We derive an error estimate showing that when the geometrical coefficients of the shell mid-surface satisfy certain conditions the finite element method has the optimal order of accuracy, which is uniform with respect to the shell thickness. Generally, the error estimate shows how the acc...

A method for identifying a piecewise-linear approximation to the nonlinear forces acting on a system is presented and demonstrated using response data from a micro cantilever beam. It is based on the Restoring Force Surface (RFS) method by Masri and Caughey, which is very attractive when initially testing a nonlinear system because it does not require the user to postulate a form for the nonlin...

The paper deals with the shape and topology optimization of the elliptic variational inequalities using the level set approach. The standard level set method is based on the description of the domain boundary as an isocountour of a scalar function of a higher dimensionality. The evolution of this boundary is governed by Hamilton-Jacobi equation. In the paper a piecewise constant level set metho...

In emission tomography, a principled means of incorporating a piecewise smooth prior on the source f is via a mixed variable objective function E(f; l) deened on f and binary valued line processes l. MAP estimation on E(f; l) results in the diicult problem of minimizing an objective function that includes a nonsmooth Gibbs prior deened on the spatial derivatives of f. Previous approaches have u...

A quasi-interpolation method for quadratic piecewise polynomials in three variables is described which can be used for the efficient visualization of gridded volume data. We analyze the smoothness properties of the trivariate splines. We prove that the splines yield nearly optimal approximation order while simultaneously its piecewise derivatives provide optimal approximation of the derivatives...

For certain classes of fractal differential equations on the Sierpinski gasket, built using the Kigami Laplacian, we describe how to approximate solutions using the finite element method based on piecewise harmonic or piecewise biharmonic splines. We give theoretical error estimates, and compare these with experimental data obtained using a computer implementation of the method (available at th...

In the present paper we generalize Eckhoff’s method, i.e., the method for approximating the locations of discontinuities and the associated jumps of a piecewise smooth function by means of its Fourier-Chebyshev coefficients. A new method enables us to approximate the locations of discontinuities and the associated jumps of a discontinuous function, which belongs to a restricted class of the pie...

Recently, pathfollowing algorithms for parametric optimization problems with piecewise linear solution paths have been developed within the field of regularized regression. This paper presents a generalization of these algorithms to a wider class of problems, namely a class of parametric piecewise quadratic programs and related problems. It is shown that the approach can be applied to the nonpa...

A two-step controller synthesis method is proposed in this paper for a class of uncertain nonlinear systems described by piecewise affine differential inclusions. In the first step, a robust linear controller is designed for the linear differential inclusion that describes the dynamics of the nonlinear system close to the equilibrium point. In the second step, a stabilizing piecewise affine con...

A new method for the three-dimensional shape recovery from image focus is proposed. The method is based on approximation of the Focussed Image Surface (FIS) by a piecewise curved surface which tracks the realistic FIS in image space. The piecewise curved surface is estimated by interpolation using the Lagrangian polynomial. The new method has been implemented on a prototype camera system. The e...