It is well known that the quasi variational inequalities are equivalent to the fixed point problems. We this equivalent alternative formulation to discuss the existence of a solution of quasi variational inequalities under some mild conditions. Since the quasi variational inequalities include variational inequalities, implicit complementarity problems and optimization problems as special cases,...

This paper discusses the variational structure of the tine contact problem between an elastic medium and a fluid. The equations for the deformation in the elastic material, and for the flow of the viscous fluid are assumed to be determined from an elastic energy E and a power functional P respectively. Then it is shown that a variational formulation of the combined system can be given: apart fr...

One of the main technique used to recover motion analysis from two images or to register them is variational optical flow, where the pixels of one image are matched to the pixels of the second image by minimizing an energy functional. In the standard formulation of variational optical flow, the estimated motion vector field depends on the reference image and is asymmetric. However, in most appl...

The purpose of this work is twofold. First, we demonstrate analytically that the classical Newmark family as well as related integration algorithms are variational in the sense of the Veselov formulation of discrete mechanics. Such variational algorithms are well known to be symplectic and momentum preserving and to often have excellent global energy behaviour. This analytical result is veri ed...

This paper presents a variational formulation of viscoplastic constitutive updates for porous elastoplastic materials. The material model combines von Mises plasticity with volumetric plastic expansion as induced, e.g., by the growth of voids and defects in metals. The finite deformation theory is based on the multiplicative decomposition of the deformation gradient and an internal variable for...

This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears and Süli [SIAM J. Numer. Anal., 51 (2013), pp. 2088–2106], and the second one is a new symmetric formulation based on a least-squares functional. These formulations enable the use of standard f...

We propose here the use of the variational level set methodology to capture Lagrangian vortex boundaries in 2D unsteady velocity fields. This method reformulates earlier approaches that seek material vortex boundaries as extremum solutions of variational problems. We demonstrate the performance of this technique for two different variational formulations built upon different notions of coherenc...

In this paper, we consider the problem of finding a zero of difference of two monotone operators in Hilbert space. Using the resolvent operator technique, we establish the equivalence between the variational inclusions and the fixed point problems. This alternative equivalent formulation is used to suggest and analyze a two-step iterative method for solving the variational inclusions involving ...