A variational framework is defined for vertical slice models with three-dimensional velocity depending only on x and z. The models that result from this framework are Hamiltonian, and have a Kelvin– Noether circulation theorem that results in a conserved potential vorticity in the slice geometry. These results are demonstrated for the incompressible Euler– Boussinesq equations with a constant t...

We present a class of constitutive updates for general viscoplastic solids including such aspects of material behavior as nite elastic and plastic deformations, non-Newtonian viscosity, rate-sensitivity and arbitrary ow and hardening rules. The distinguishing characteristic of the proposed constitutive updates is that, by construction, the corresponding incremental stress-strain relations deriv...

It has been known since the early 1970s that the Hessian matrices in quasi– Newton methods can be updated by variational means, in several different ways. The usual formulation of these variational problems uses a coordinate system, and the symmetry of the Hessian matrices are enforced as explicit constraints. As a result, the variational problems seem complicated. In this paper, we give a very...

In this paper, we consider a new class of quasi variational inequalities involving three operators, which is called the extended general quasi variational inequality. It is shown that the extended general quasi variational inequalities are equivalent to the fixed problems. This equivalence is used to suggest and analyze some iterative methods for solving the extended general quasi variational i...

In this paper we discuss the connections between a Vlasov-Fokker-Planck equation and an underlying microscopic particle system, and we interpret those connections in the context of the GENERIC framework (Öttinger 2005). This interpretation provides (a) a variational formulation for GENERIC systems, (b) insight into the origin of this variational formulation, and (c) an explanation of the origin...

In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions when applied to one-dimensional problems with constant coefficients and forcing function. We first present a variational principle for a multi-dimensional advec...

In this paper we deal with existence and uniqueness of solution to super-linear problems for the Pucci operator: −M(Du) + |u|u = f(x) in IR, where s > 1 and f satisfies only local integrability conditions. This result is well known when, instead of the Pucci operator, the Laplacian or a divergence form operator is considered. Our existence results use the Alexandroff-Bakelman-Pucci inequality s...

Computational fluid mechanics based on the finite element method has been developed so far following two distinct approaches (a) using a stream function, or stream functlon-vortlcity formulation [1,2], and (b) using a primitive variables formulation [3,4,5]. Within the first approach a stream function is defined such that the continuity equation is identically satisfied and the momentum equatio...

The ultra weak variational formulation (UWVF) approach has been proposed as an effective method for solving Helmholtz problems with high wave numbers. However, for coarse meshes the method can suffer from instability. In this paper we consider computational aspects of the ultra weak variational formulation for the inhomogeneous Helmholtz problem. We introduce a method to improve the UWVF scheme...

We propose an approach to perform orbital-free density functional theory calculations in a nonperiodic setting using the finite-element method. We consider this a step towards constructing a seamless multi-scale approach for studying defects like vacancies, dislocations and cracks that require quantum mechanical resolution at the core and are sensitive to long range continuum stresses. In this ...