Combining the variational multiscale (VMS) method for large-eddy simulation with a discontinuous Galerkin (DG) spatial discretization leads to a synergistic approach to turbulence simulation that we call the local variational multiscale (`VMS) method. In `VMS the flexibility of DG enables the large and small-scale spaces to be set on each element independently. In this paper, preliminary result...

In this paper, we apply the modified variational iteration method (mVIM) for solving integrodifferential equations and coupled systems of integro-differential equations. The proposed modification is made by the elegant coupling of He’s polynomials and the correction functional of variational iteration method. The proposed mVIM is applied without any discretization, transformation or restrictive...

We consider a variational formulation of the three-dimensional Navier–Stokes equations with mixed boundary conditions and prove that the variational problem admits a solution provided that the domain satisfies a suitable regularity assumption. Next, we propose a finite element discretization relying on the Galerkin method and establish a priori and a posteriori error estimates. Mathematics Subj...

In this paper, variational iteration method is applied for finding the solution of differential equations with piecewise constant arguments. A correction functional is constructed by a general Lagrange multiplier, which can be identified by variational theory. This technique provides a sequence of functions which converges to the exact solution of the problem without discretization of the varia...

We report results of a Monte Carlo simulation of the φ4 quantum chain. In order to enhance the efficiency of the simulation we combine multigrid simulation techniques with a refined discretization scheme. The resulting accuracy of our data allows for a significant test of an analytical approximation based on a variational ansatz. While the variational approximation is well reproduced for a larg...

CCC 0749-159X/93/010023-11 Numerical Methods for Partial Differential Equations, 9, 23-33 (1993) \!:) 1993 John Wiley & Sons, Inc. Local a posteriori error estimators for finite element approximation o( variational inequalities are derived. These are shown to provide upper bounds on the discretization error. Numerical examples are given illustrating the theoretical results. © 1993 John Wiley an...

Casting nonlocal problems in variational form and discretizing them with the finite element (FE) method facilitates use of vector calculus to prove well-posedeness, convergence, stability such schemes. Employing an FE also meshing complicated domain geometries coupling methods for local problems. However, weak involve computation a double-integral, which is computationally expensive presents se...

This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions. Firstly, the problem is reduced to an equivalent problem which is easy to handle using variational iteration method. Secondly, variational iteration method is used to solve the reduced problem. Using this method a rapid convergent sequence can be produced which ten...

Here, p(: Ω→ R) is the pressure, ∂Ω is the boundary, and n is the unit outward normal vector on ∂Ω. In the axisymmetric case, the existence of solutions to (1.2) was discussed as the problem of vortex rings in, for example, [2, 4, 5, 8]. Their methods were based on a variational principle for kinetic energy. By contrast, Vallis et al. [13] proposed a completely different approach to the solvabi...

The aim of this paper is to study the continuity of the solutions to degenerate time-dependent variational inequalities. In order to obtain the continuity of the solution, a previous continuity result (see [1]) for strongly monotone variational inequalities and an appropriate use of the convergence set in Mosco’s sense play an important role. The continuity result allows us to provide a discret...