In earlier work we have studied a method for discretization in time of a parabolic problem, which consists of representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In application to a spatially semidiscrete finite-element version of the parabolic problem, at each quadrature point one then needs to solve a linear algebraic sy...

Existing deenitions of backward error and condition number for linear systems do not cater for structure in the coeecient matrix, except possibly for sparsity. We extend the deenitions so that when the coeecient matrix has structure the perturbed matrix has this structure too. We show that when the structure comprises linear dependence on a set of parameters the structured componentwise backwar...

A mesh-independent, robust, and accurate multigrid scheme to solve a linear state-constrained parabolic optimal control problem is presented. We first consider a Lavrentiev regularization of the state-constrained optimization problem. Then, a multigrid scheme is designed for the numerical solution of the regularized optimality system. Central to this scheme is the construction of an iterative p...

We consider a non degenerate quasilinear parabolic stochastic partial differential equation with a uniformly elliptic diffusion matrix. It is driven by a nonlinear noise. We study regularity properties of its weak solution satisfying classical a priori estimates. In particular, we determine conditions on coefficients and initial data under which the weak solution is Hölder continuous in time an...

We derive the precise limit of SHS in the high activation energy scaling suggested by B.J. Matkowksy-G.I. Sivashinsky in 1978 and by A. Bayliss-B.J. Matkowksy-A.P. Aldushin in 2002. In the time-increasing case the limit coincides with the Stefan problem for supercooled water with spatially inhomogeneous coefficients. In general it is a nonlinear forward-backward parabolic equation with disconti...

We consider the backward error associated with a given approximate solution of a linear least squares problem. The backward error can be very expensive to compute, as it involves the minimal singular value of certain matrix that depends on the problem data and the approximate solution. An estimate based on a regularized projection of the residual vector has been proposed in the literature and a...

In this paper we revisit the parabolic approximation for wave propagation in random media by taking into account backscattering. We obtain a system of transport equations for the moments of the components of reflection and transmission operators. In the regime in which forward scattering is strong and backward scattering is weak, we obtain closed form expressions for physically relevant quantit...

We analyze stability properties of BDF methods of order up to 5 for linear parabolic equations as well as of implicit–explicit BDF methods for nonlinear parabolic equations by energy techniques; time dependent norms play also a key role in the analysis.

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical KazhdanLusztig theory. We further verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category O of the general linear supera...

We investigate the optimal control problem with respect to coefficients of degenerate parabolic variational inequality. Since problems this type can have Lavrentieff effect, we consider in a class so-called Hadmissible solutions. substantiate attainability H-optimal pairs via solutions some nondegenerate perturbed problems.