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Rob Stevenson 《Numerische Mathematik》2002,91(2):351-387
Summary. We derive sufficient conditions under which the cascadic multi-grid method applied to nonconforming finite element discretizations
yields an optimal solver. Key ingredients are optimal error estimates of such discretizations, which we therefore study in
detail. We derive a new, efficient modified Morley finite element method. Optimal cascadic multi-grid methods are obtained
for problems of second, and using a new smoother, of fourth order as well as for the Stokes problem.
Received February 12, 1998 / Revised version received January 9, 2001 / Published online September 19, 2001 相似文献
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Summary. In this paper, we derive a posteriori error estimates for the finite element approximation of quadratic optimal control problem
governed by linear parabolic equation. We obtain a posteriori error estimates for both the state and the control approximation.
Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive
finite element approximation schemes for the control problem.
Received July 7, 2000 / Revised version received January 22, 2001 / Published online January 30, 2002
RID="*"
ID="*" Supported by EPSRC research grant GR/R31980 相似文献
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Summary. In this paper, we derive quasi-norm a priori and a posteriori error estimates for the Crouzeix-Raviart type finite element
approximation of the p-Laplacian. Sharper a priori upper error bounds are obtained. For instance, for sufficiently regular
solutions we prove optimal a priori error bounds on the discretization error in an energy norm when . We also show that the new a posteriori error estimates provide improved upper and lower bounds on the discretization error.
For sufficiently regular solutions, the a posteriori error estimates are further shown to be equivalent on the discretization
error in a quasi-norm.
Received January 25, 1999 / Revised version received June 5, 2000 Published online March 20, 2001 相似文献
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We prove that if a metric probability space with a usual concentration property embeds into a finite dimensional Banach space
X, then X has a Euclidean subspace of a proportional dimension. In particular this yields a new characterization of weak cotype 2.
We also find optimal lower estimates on embeddings of metric spaces with concentration properties into , generalizing estimates of Bourgain—Lindenstrauss—Milman, Carl—Pajor and Gluskin.
Submitted: February 2001, Revised: August 2001. 相似文献
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Marc Küther 《Numerische Mathematik》2003,93(4):697-727
Summary. We introduce a new technique for proving a priori error estimates between the entropy weak solution of a scalar conservation
law and a finite–difference approximation calculated with the scheme of Engquist-Osher, Lax-Friedrichs, or Godunov. This technique
is a discrete counterpart of the duality technique introduced by Tadmor [SIAM J. Numer. Anal. 1991]. The error is related
to the consistency error of cell averages of the entropy weak solution. This consistency error can be estimated by exploiting
a regularity structure of the entropy weak solution. One ends up with optimal error estimates.
Received December 21, 2001 / Revised version received February 18, 2002 / Published online June 17, 2002 相似文献
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Reward functionals, salvage values, and optimal stopping 总被引:2,自引:0,他引:2
Luis H. R. Alvarez 《Mathematical Methods of Operations Research》2001,54(2):315-337
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Chen Wei 《Numerical Methods for Partial Differential Equations》2001,17(2):93-104
Implicit‐explicit multistep finite element methods for nonlinear convection‐diffusion equations are presented and analyzed. In space we discretize by finite element methods. The discretization in time is based on linear multistep schemes. The linear part of the equation is discretized implicitly and the nonlinear part of the equation explicitly. The schemes are stable and very efficient. We derive optimal order error estimates. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:93–104, 2001 相似文献
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Summary. For evolution equations with a strongly monotone operator we derive unconditional stability and discretization error estimates valid for all . For the -method, with , we prove an error estimate , if , where is the maximal integration step for an arbitrary choice of sequence of steps and with no assumptions about the existence
of the Jacobian as well as other derivatives of the operator , and an optimal estimate under some additional relation between neighboring steps. The first result is an improvement over the implicit midpoint method
, for which an order reduction to sometimes may occur for infinitely stiff problems. Numerical tests illustrate the results.
Received March 10, 1999 / Revised version received April 3, 2000 / Published online February 5, 2001 相似文献
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In this paper we investigate POD discretizations of abstract linear–quadratic optimal control problems with control constraints.
We apply the discrete technique developed by Hinze (Comput. Optim. Appl. 30:45–61, 2005) and prove error estimates for the corresponding discrete controls, where we combine error estimates for the state and the
adjoint system from Kunisch and Volkwein (Numer. Math. 90:117–148, 2001; SIAM J. Numer. Anal. 40:492–515, 2002). Finally, we present numerical examples that illustrate the theoretical results. 相似文献