We introduce a uniformly convergent iterative method for the systems arising from non-symmetric IIPG linear approximations of second order elliptic problems. The method can be viewed as a block Gauss-Seidel method in ...
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ISBN:
(纸本)9783642113031
We introduce a uniformly convergent iterative method for the systems arising from non-symmetric IIPG linear approximations of second order elliptic problems. The method can be viewed as a block Gauss-Seidel method in which the blocks correspond to restrictions of the IIPG method to suitably constructed subspaces. Numerical tests are included, showing the uniform convergence of the iterative method in an energy norm.
A singularly perturbed degenerate parabolic problem is considered. The behaviour of its solution u depends on three parameters that are determined by the data of the problem. Theoretical bounds on u are stated in term...
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ISBN:
(纸本)9783642196645
A singularly perturbed degenerate parabolic problem is considered. The behaviour of its solution u depends on three parameters that are determined by the data of the problem. Theoretical bounds on u are stated in terms of these parameters and extensive numerical experiments verify the sharpness of these bounds.
In this work, we report on an ongoing project to implement an hp-adaptive finite element method. The inspiration of this work came from the development of certain a posteriori error estimates for high order finite ele...
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We study the performance properties of a class of stabilized higher-order finite element approximations of convection-diffusion-reaction models with nonlinear reaction mechanisms. Streamline upwind Petrov-Galerkin (SU...
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ISBN:
(数字)9783642196652
ISBN:
(纸本)9783642196645
We study the performance properties of a class of stabilized higher-order finite element approximations of convection-diffusion-reaction models with nonlinear reaction mechanisms. Streamline upwind Petrov-Galerkin (SUPG) stabilization together with anisotropic shock-capturing as an additional stabilization in crosswind-direction is used. We show that these techniques reduce spurious oscillations in crosswind-direction and increase the accuracy of simulations.
We consider traces and discrete harmonic extensions on thin boundary layers. We introduce sharp estimates on how to control the H-1/2 - or H-00(1/2) - boundary norm of a finite element function by its energy in a thin...
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ISBN:
(纸本)9783642113031
We consider traces and discrete harmonic extensions on thin boundary layers. We introduce sharp estimates on how to control the H-1/2 - or H-00(1/2) - boundary norm of a finite element function by its energy in a thin layer and vice versa, how to control the energy of a discrete harmonic function in a layer by the H-1/2 or H-00(1/2) norm on the boundary. Such results play an important role in the analysis of domain decomposition methods in the presence of high-contrast media inclusions, small overlap and/or inexact solvers.
A stable boundary element tearing and interconnecting domain decomposition method is considered for the parallel solution of the Helmholtz equation. In particular, we discuss the preconditioned iterative solution of t...
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ISBN:
(纸本)9783642113031
A stable boundary element tearing and interconnecting domain decomposition method is considered for the parallel solution of the Helmholtz equation. In particular, we discuss the preconditioned iterative solution of the resulting linear system and present some numerical results.
In this paper, we construct an auxiliary space preconditioner for Maxwell's equations with interface, and generalize the HX preconditioner developed in [9] to the problem with strongly discontinuous coefficients. ...
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ISBN:
(纸本)9783642113031
In this paper, we construct an auxiliary space preconditioner for Maxwell's equations with interface, and generalize the HX preconditioner developed in [9] to the problem with strongly discontinuous coefficients. For the H(curl) interface problem, we show that the condition number of the HX preconditioned system is uniformly bounded with respect to the coefficients and meshsize.
We consider the coupling across an interface of a fluid flow and a porous media flow. The differential equations involve Stokes equations in the fluid region,Darcy equations in the porous region, plus a coupling throu...
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We introduce a family of parallel Newton-Krylov-Schwarz methods for solving complementarity problems. The methods are based on a smoothed grid sequencing method, a semismooth inexact Newton method, and a two-grid rest...
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ISBN:
(纸本)9783642113031
We introduce a family of parallel Newton-Krylov-Schwarz methods for solving complementarity problems. The methods are based on a smoothed grid sequencing method, a semismooth inexact Newton method, and a two-grid restricted overlapping Schwarz preconditioner. We show numerically that such an approach is highly scalable in the sense that the number of Newton iterations and the number of linear iterations are both nearly independent of the grid size and the number of processors. In addition, the method is not sensitive to the sharp discontinuity that is often associated with obstacle problems. We present numerical results for some large scale calculations obtained on machines with hundreds of processors.
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