Richard Liska

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The results of computations with eight explicit finite difference schemes on a suite of one-dimensional and two-dimensional test problems for the Euler equations are presented in various formats. Both dimensionally split and two-dimensional schemes are represented, as are central and upwind-biased methods, and all are at least second-order accurate.
In this paper we show how a number of interesting linear control system analysis and design problems can be reduced to Quantiier Elimination (QE) problems. We assume a xed structure for the compensator, with design parameters q i. The problems considered are problems that currently have no general solution. However, the problems must be of modest complexity(More)
The maximum principle is a basic qualitative property of the solution of second-order elliptic boundary value problems. The preservation of the qualitative characteristics, such as the maximum principle, in discrete model is one of the key requirements. It is well known that standard linear finite element solution does not satisfy maximum principle on(More)
A new optimization-based synchronized flux-corrected conservative interpolation (remapping) of mass and momentum for arbitrary Lagrangian–Eulerian hydro methods is described. Fluxes of conserved variables – mass and momentum – are limited in a synchronous way to preserve local bounds of primitive variables – density and velocity. Published by Elsevier Inc.
The support operator method designs mimetic finite difference schemes by first constructing a discrete divergence operator based on the divergence theorem, and then defining the discrete gradient operator as the adjoint operator of the divergence based on the Gauss theorem connecting the divergence and gradient operators, which remains valid also in the(More)
The paper deals with the formalization of the basic operator method for construction of difference schemes for the numerical solving of partial differential eq~uations. The strength of the basic operator method lies on the fact that it produces fully conservative difference schemes. The difference mesh can be non-orthogonal but has to be logically(More)
The maximum principle is basic qualitative property of the solution of elliptic boundary value problems. The preservation of the qualitative characteristics, such as maximum principle, in discrete model is one of the key requirements. It is well known that standard linear finite element solution does not satisfy maximum principle on general triangular(More)
First-order constraints over the reals appear in numerous contexts. Usually existential quantification occurs when some parameter can be chosen by the user of a system, and univeral quantification when the exact value of a parameter is either unknown, or when it occurs in infinitely many, similar versions. The following is a list of application areas and(More)