In this paper we present an adaptive strategy to obtain an incompressible wind field that adjusts to an experimental one, and verify boundary conditions of physical interest. We use an Augmented Lagrangian formulation for solving this problem. Our method is based on an Uzawa iteration to update the Lagrange multiplier and on an elliptic adaptive inner iteration for velocity. Several examples sh...

We present a mixed finite element method for the thin film epitaxy problem. Comparing to the primal formulation which requires C2 elements in the discretization, the mixed formulation only needs to use C1 elements, by introducing proper dual variables. The dual variable in our method is defined naturally from the nonlinear term in the equation, and its accurate approximation will be essential f...

and Applied Analysis 3 Table 1: Solitary wave Amp. 0.3 and the errors in L2 and L∞ norms for u, Q 1 , Q 2 , and Q 3 at t = 20, h = 0.125, Δt = 0.1, and −40 ≤ x ≤ 60. Method Time Q 1 Q 2 Q 3 L 2 for u L∞ for u Our method 0 3.9797 0.8104 2.5787 0 0 4 3.9797 0.8104 2.5786 3.6304e − 004 5.2892e − 005 8 3.9797 0.8104 2.5786 7.2873e − 004 5.8664e − 005 12 3.9797 0.8104 2.5787 1.0817e − 003 6.3283e − ...

In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces....

in this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. we prove a posteriori $ l^2(l^2)$ and error estimates for this method under minimal regularity hypothesis. test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.

in this paper, based on the slab method of analysis, a novel and general approach isdeveloped for studying the radial forging process with curved profile dies. the presented approachis not only more general with respect to previous studies, but it is also easier to understand and useand can be efficiently used for optimization of the die profile depending on the forging geometryand conditions. ...

We provide some extensions to the AMGe method (algebraic multigrid method based on element interpolation), concerning the agglomeration process, the application to non-conforming elements, and the application to the mixed finite element discretization of the Oseen-linearized Navier-Stokes equations. This last point, using AMGe for mixed finite elements, gets straight-forward because of the avai...

A two-grid scheme based on mixed finite-element approximations to the incompressible Navier-Stokes equations is introduced and analyzed. In the first level the standard mixed finite-element approximation over a coarse mesh is computed. In the second level the approximation is postprocessed by solving a discrete Oseen-type problem on a finer mesh. The two-level method is optimal in the sense tha...

This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear vector fields for displacement, this gives a stable mixed finite element method which is shown to be linearly convergent for both the stress and displacement, an...

The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...