Averaging techniques for finite element error control, occasionally called ZZ estimators for the gradient recovery, enjoy a high popularity in engineering because of their striking simplicity and universality: One does not even require a PDE to apply the nonexpensive postprocessing routines. Recently, averaging techniques have been mathematically proved to be reliable and efficient for various ...

Keywords: Rotating Navier–Stokes equations Exterior domain Boundary integral method Finite element approximation a b s t r a c t In this paper, we apply the boundary integral method to the linearized rotating Navier– Stokes equations in exterior domain. Introducing some open ball which decomposes the exterior domain into a finite domain and an infinite domain, we obtain a coupled problem by the...

This paper presents a new set of boundary integral equations for three dimensional acoustic shape sensitivity analysis based on the direct differentiation method. A linear combination of the derived equations is used to avoid the fictitious eigenfrequency problem associated with the conventional boundary integral equation method when solving exterior acoustic problems. The strongly singular and...

I review progress related to the calculation of QCD jet cross sections at the NLO accuracy. After a short introduction into the theory of NLO calculations, I discuss two recent developments: the calculation of twoand three-jet leptoproduction at the NLO accuracy and the extension of the dipole subtraction method for computing NLO corrections for processes involving massive partons. Jet cross se...

A model is provided for crack problem in a functionally graded semi-infinite plate under an anti-plane load. The characteristic of material behavior is assumed to change in a linear manner along the plate length. Also the embedded crack is placed in the direction of the material change. The problem is solved using two separate techniques. Primary, by applying Laplace and Fourier transformation,...

The Karhunen-Loève expansion of a Gaussian process, a common tool on finite element methods for differential equations with stochastic coefficients, is based on the spectral decomposition of its covariance function. The eigenpairs of the covariance are expressed as a Fredholm integral equation of second kind, which can be readily approximated with piecewise-constant finite elements. In this wor...

The two-dimensional problem of advection–dispersion associated with a non-aqueousphase liquid (NAPL) pool is addressed using the boundary element method. The problem is appropriately posed with an inhomogeneous boundary condition taking into consideration the presence of the pool and the impermeable layer. We derive a Fredholm integral equation of the first kind for the concentration gradient a...

Within the path integral approach quantum field theory can be formulated as an integral over the superspace of fields. The Berezin integral is the crucial element in this construction. Replacing an infinite-dimensional supermanifold of fields by an ordinary supermanifold we get a nice toy model of quantum field theory. In this article I motivate the origin of the Berezin integral and trace some...

Multigrid methods are typically used to solve partial differential equations, i.e., they approximate the inverse of the corresponding partial differential operators. At least for elliptic PDEs, this inverse can be expressed in the form of an integral operator by Green's theorem. This implies that multigrid methods approximate certain integral operators , so it is straightforward to look for var...