In this paper, we combine continuous Galerkin-Petrov (cGP) and discontinuous Galerkin (dG) time stepping schemes with local projection method applied to inf-sup stable discretization of the transient Oseen problem. Using variational-type time-discretization methods of polynomial degree k, we show that the cGP(k) and dG(k) methods are accurate of order k+1, in the whole time interval. Moreover, ...

In the present work, we apply a variational discretization proposed by the first author in [14] to Lavrentiev-regularized state constrained elliptic control problems. We extend the results of [18] and prove weak convergence of the adjoint states and multipliers of the regularized problems to their counterparts of the original problem. Further, we prove error estimates for finite element discret...

We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulat...

We consider a stationary Stokes problem with a piecewise constant viscosity coefficient. For the variational formulation of this problem in H0 × L2 we prove a well-posedness result in which the constants are uniform with respect to the jump in the viscosity coefficient. For a standard discretization with a pair of LBB stable finite element spaces we prove an infsup stability result uniform with...

In this paper, we apply the variational iteration method using He’s polynomials for finding the analytical solution of gas dynamic equation. The proposed method is an elegant combination of He’s variational iteration and the homotopy perturbation methods. The suggested algorithm is quite efficient and is practically well suited for use in such problems. The proposed iterative scheme finds the s...

A few years ago, Costabel and Dauge proposed a variational setting, which allows one to solve numerically the time-harmonic Maxwell equations in 3D geometries with the help of a continuous approximation of the electromagnetic field. In this paper, we investigate how their framework can be adapted to compute the solution to the time-dependent Maxwell equations. In addition, we propose some exten...

In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by a suitable frame decomposition of the solution, i.e., a complete, stable, and redundant expansion. The discretization yields an equivalent nonlinear problem on ℓ2(N), the space of frame coefficients. The discrete problem is then adaptively sol...

This paper is concerned with numerical solutions to a singular stochastic control problem arising from the continuous-time portfolio selection with proportional transaction costs. The associated value function is governed by a variational inequality with gradient constraints. We propose a penalty method to deal with the gradient constraints and employ a finite difference discretization. Converg...

In this contribution we review a posteriori based discretization methods for variational multiscale problems and suggest a suitable conceptual approach for an efficient numerical treatment of parametrized variational multiscale problems where the parameters are either chosen from a low dimensional parameter space or consists of parameter functions from some compact low dimensional manifold that...

In this paper, the variational iteration method (VIM) is applied for solving the fifth order Caudrey-Dodd-Gibbon (CDG) equation. We obtain the approximate solutions without unrealistic nonlinear assumptions , linearization, discretization or the calculation of Adomian's poly-nomials. Numerical results are presented to verify the efficiency of the VIM.