The current work concerns the study and the implementation of a modern algorithm for error estimation in CFD computations. This estimate involves the dealing of the adjoint argument. By solving the adjoint problem, it is possible to obtain important information about the transport of the error towards the quantity of interest. The aim is to apply for the first time this procedure into Petrov-Ga...

In recent years, there have been extensive efforts to find the numerical methods for solving problems with interface. The main idea of this work is to introduce an efficient truly meshless method based on the weak form for interface problems. The proposed method combines the direct meshless local Petrov–Galerkin method with the visibility criterion technique to solve the interface problems. It ...

We present optimal error estimates for spectral Petrov–Galerkin methods and spectral collocation methods for linear fractional ordinary differential equations with initial value on a finite interval. We also develop Laguerre spectral Petrov–Galerkin methods and collocation methods for fractional equations on the half line. Numerical results confirm the error estimates.

Abstract In this contribution, it is demonstrated that the mesh sensitivity of linear elastic Reissner–Mindlin finite‐element plate formulations can be significantly reduced by using a Petrov–Galerkin‐based approach. contrast to usual Bubnov–Galerkin method, Petrov–Galerkin methods are generally characterized fact test function and trial approximated different shape functions. To provide an ove...

V. A. PETROV AND A. V. PROKUDIN Institute For High Energy Physics, 142284 Protvino , Russia E-mail: [email protected] [email protected] We develop an off-shell extention of the Regge-eikonal approach which automatically takes into account off-shell unitarity. We argue that exclusive vector-meson production cross-sections measured at HERA can be fairly described with classical universal Regge...

We shall use the quantities and notation stated in [1]. The Petrov classification (PC) [1-8] of the Weyl tensor has a great importance in general relativity, thus it is attractive to account with an efficient procedure to determine the Petrov type of an arbitrary gravitational field. Peres [9] has worked out the tensorial version of the Petrov’s matrix approach [2-4] to perform the PC. In the f...

Some consequences which follow from the periodicity assumption for spectral density of Wilson–Dirac operator are studied. Such an assumption allows to obtain simple representations for quark propagator, which reveals an important role of m ↔ −m symmetry. It is argued that this symmetry is restored when the mirror fermion mass mr tended to infinity. The constrains on zero modes of Wilson–Dirac o...

We develop an algebraic procedure to rotate a general NewmanPenrose tetrad in a Petrov type I spacetime into a frame with Weyl scalars Ψ1 and Ψ3 equal to zero, assuming that initially all the Weyl scalars are non vanishing. The new frame highlights the physical properties of the spacetime. In particular, in a Petrov Type I spacetime, setting Ψ1 and Ψ3 to zero makes apparent the superposition of...

A Legendre and Chebyshev dual-Petrov–Galerkin method for hyperbolic equations is introduced and analyzed. The dual-Petrov– Galerkin method is based on a natural variational formulation for hyperbolic equations. Consequently, it enjoys some advantages which are not available for methods based on other formulations. More precisely, it is shown that (i) the dual-Petrov–Galerkin method is always st...

This paper analyzes a method for solving the thirdand fifth-order differential equations with constant coefficients using a Jacobi dual-Petrov–Galerkin method, which is more reasonable than the standard Galerkin one. The spatial approximation is based on Jacobi polynomials P (α,β) n with α, β ∈ (−1, ∞) and n is the polynomial degree. By choosing appropriate base functions, the resulting system ...