A new error control finite element formulation is developed and implemented based on the variational multiscale method, the inclusion theory in homogenization, and the Zienkiewicz–Zhu error estimator. By synthesizing variational multiscale method in computational mechanics, the equivalent eigenstrain principle in micromechanics, and the Zienkiewicz–Zhu error estimator in the finite element meth...

The theoretical formulation of the variational bounds on scattering parameters is briefly reviewed. The upper and lower bounds on scattering parameters are realized by the manner in which the distortion of the target during the scattering is treated, in terms of the static and adiabatic pictures. The variational bounds are obtained by gradually improving the trial functions that describe the ta...

The theory of the gap functions is extended to the variational inequality introduced by Minty. Exploiting the minimax formulation of a variational inequality, a new class of gap functions is defined. Descent methods,based on the minimization of the new class of gap functions, are analysed.

In this paper, we prove that the general quasi variational inequalities are equivalent to the fixed point problem using the projection technique. We use this equivalent formulation to study the sensitivity analysis of the general quasi variational inequality. Our approach is very simple. Several special cases are also discussed. AMS subject classifications: 49J40, 90C33

It is well known that the implicit resolvent equations are equivalent to the quasivariational inclusions. We use this alternative equivalent formulation to study the sensitivity of the quasi-variational inclusions without assuming the differentiability of the given data. Since the quasivariational inclusions include classical variational inequalities, quasi (mixed) variational inequalities, and...

The objectives of recent variational multiscale work in turbulence have been to capture all scales consistently and to avoid use of eddy viscosities altogether. This holds the promise of more accurate and efficient LES procedures. In this work, we describe a new variational multiscale formulation, which makes considerable progress toward these goals.

We show by direct calculation that the replica and cavity methods are exactly equivalent for the spectrum of an Erdős-Rényi random graph. We introduce a variational formulation based on the cavity method and use it to find approximate solutions for the density of eigenvalues. We also use this variational method for calculating spectra of sparse covariance matrices.

Gaussian process classification is a popular method with a number of appealing properties. We show how to scale the model within a variational inducing point framework, outperforming the state of the art on benchmark datasets. Importantly, the variational formulation can be exploited to allow classification in problems with millions of data points, as we demonstrate in experiments.

This article presents a formulation of the time-fractional generalized Korteweg-de Vries (KdV) equation using the Euler-Lagrange variational technique in the Riemann-Liouville derivative sense. It finds an approximate solitary wave solution, and shows that He’s variational iteration method is an efficient technique in finding the solution.

In the variational formulation of finite element models for mechanics problems, boundary conditions are classified as either essential or natural. The traction boundary conditions are identified as natural in many commonly-used finite element models. A valid finite element mode must satisfy explicitly the essential boundary conditions, since the latter are satisfied implicitly as a posteriori c...