This work proves rigorous results about the vanishing mass limit of classical problem to find a shape with minimal elastic compliance. Contrary all previous in mathematical literature, which utilize soft constraint by introducing Lagrange multiplier, we here consider hard constraint. Our are first establish convergence approximately optimal shapes (exact) size ??0 generalized represented (possi...

A quasi-interpolation formula based on discrete function values is given in the form of a multivariate spline series that yields the local approximation order characterized by the Fix-Strang conditions. This formula can be considered as a partial sum of the formal Neumann series expansion of the formal interpolation operator, and hence, justifies that "quasi-interpolation" is indeed an appropri...

The present work is concerned with the efficient time integration of nonlinear evolution equations by exponential operator splitting methods. Defect-based local error estimators serving as a reliable basis for adaptive stepsize control are constructed and analyzed. In the context of time-dependent nonlinear Schrödinger equations, asymptotical correctness of the local error estimators associated...

Two families of limited-memory variable metric or quasi-Newton methods for unconstrained minimization based on quasi-product form of update are derived. As for the first family, four variants how to utilize the Strang recurrences for the Broyden class of variable metric updates are investigated; three of them use the same number of stored vectors as the limitedmemory BFGS method. Moreover, one ...

This paper is concerned with the existence of minimizers for functionals having a double-well integrand with affine boundary conditions. Such functionals are related to the so-called Kohn-Strang functional which arises in optimal shape design problems in electrostatics or elasticity. They are known to be not quasi-convex, and therefore existence of minimizers is, in general, guaranteed only for...