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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)
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 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)
A new optimization-based synchronized flux-corrected conservative interpolation (remap-ping) 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. In numerical simulations(More)
The article deals with automation of the process of numerical solving of partial differential equations systems (PDES) by means of computer algebra. For solving PDES the finite difference method is applied. The computer algebra system REDUCE and the numerical programming language FORTRAN are used in the methodology presented, its main aim being to speed up(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)