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We present a parallel nonoverlapping Schwarz domain decomposition method with interface relaxation for linear elliptic problems, possibly with discontinuities in the solution and its derivatives. This domain decomposition method can be characterized as: the transmission conditions at the interface of subdomains are taken to be Dirichlet at odd iterations(More)
A parallel iterative nonoverlapping domain decomposition method is proposed and analyzed for elliptic problems. Each iteration in this method contains two steps. In the rst step, at the interface of two subdomains, one subdomain problem requires that Dirichlet data be passed to it from the previous iteration level, while the other subdomain problem requires(More)
The wave equation with attenuation due to a linear friction is approximated by a new mixed nite element method which allows one to use diierent grids and basis functions at diierent times when necessary. This method enables one to track sharp moving wave fronts more eeciently and accurately. Error estimates with optimal convergent rates are established.(More)
In this study we analyze a non-overlapping domain decomposition method for the solution of elliptic Partial Diierential Equation (PDE) problems. This domain decomposition method involves the solution of Dirichlet and Neumann PDE problems on each subdomain, coupled with smoothing operations on the interfaces of the subdomains. The convergence analysis of the(More)
The miscible displacement problem in porous media is modeled by a nonlinear coupled system of two partial diierential equations: the pressure-velocity equation and the concentration equation. An iterative perturbation procedure is proposed and analyzed for the pressure-velocity equation, which is capable of producing as accurate velocity approximation as(More)
Stabilized iterative schemes for mixed nite element methods are proposed and analyzed in two abstract formulations. The rst one has applications to elliptic equations and incompressible uid ow problems, while the second has applications to linear elasticity and compressible Stokes problems. Convergence theorems are demonstrated in abstract formulations;(More)
Lions' non-overlapping Schwarz domain decomposition method based on a nite diierence discretization is applied to problems with fronts or layers. For the purpose of getting accurate approximation of the solution by solving small linear systems, grid reenement is made on sub-domains that contain fronts and layers and uniform coarse grids are applied on(More)
A parallel nonoverlapping Schwarz algorithm based on a nite element discretization is applied to convection diiusion problems with fronts and layers. At inter-domain boundaries, a Robin type boundary condition is weakly imposed into the nite element variational form. Grid reenement is made on subdomains that contain fronts and layers and coarse grids are(More)