Pii: S0168-9274(01)00161-1
نویسندگان
چکیده
In this paper, we study time discretizations of fully nonlinear parabolic differential equations. Our analysis uses the fact that the linearization along the exact solution is a uniformly sectorial operator. We derive smooth and nonsmooth-data error estimates for the backward Euler method, and we prove convergence for strongly A(θ)stable Runge–Kutta methods. For the latter, the order of convergence for smooth solutions is essentially determined by the stage order of the method. Numerical examples illustrating the convergence estimates are presented. 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.
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Pii: S0168-9274(01)00134-9
A postprocessing technique to improve the accuracy of Galerkin methods, when applied to dissipative partial differential equations, is examined in the particular case of very smooth solutions. Pseudospectral methods are shown to perform poorly. This performance is studied and a refined postprocessing technique is proposed. 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.
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We present in this paper optimal and accelerated row projection algorithms arising from the use of quadratic programming, that allow us to define the iterate xk+1 as the projection of x onto a hyperplane which minimizes its distance to the solution x∗. These algorithms also use a novel partition strategy into blocks based on sequential estimations of their condition numbers. 2001 IMACS. Publi...
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An energy-preserving explicit extension operator is proposed to extend finite element functions defined on the boundary of a star-shaped polygonal domain into its interior. The pre-assigned finite element triangulation in the interior of the domain needs not be multilevel-structured. The extension operator has wide applications in the construction of non-overlapping domain decomposition methods...
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The aim of this work is to present a nonstandard linear finite element method for a planar elasticity problem. The error for the solution computed with this method is estimated with respect to H 1 ×H 1-norm and second-order convergence is shown. 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.
متن کاملPii: S0168-9274(99)00020-3
We compare several methods for sensitivity analysis of differential–algebraic equations (DAEs). Computational complexity, efficiency and numerical conditioning issues are discussed. Numerical results for a chemical kinetics problem arising in model reduction are presented. 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.
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