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1.
In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results. 相似文献
2.
Zi‐Niu Wu 《国际流体数值方法杂志》2005,48(5):541-564
The widely used locally adaptive Cartesian grid methods involve a series of abruptly refined interfaces. In this paper we consider the influence of the refined interfaces on the steady state errors for second‐order three‐point difference approximations of flow equations. Since the various characteristic components of the Euler equations should behave similarly on such grids with regard to refinement‐induced errors, it is sufficient enough to conduct the analysis on a scalar model problem. The error we consider is a global error, different to local truncation error, and reflects the interaction between multiple interfaces. The steady state error will be compared to the errors on smooth refinement grids and on uniform grids. The conclusion seems to support the numerical findings of Yamaleev and Carpenter (J. Comput. Phys. 2002; 181: 280–316) that refinement does not necessarily reduce the numerical error. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
3.
A time discrete scheme is used to approximate the solution toa phase field system of PenroseFife type with a non-conservedorder parameter. An a posteriori error estimate is presentedthat allows the estimation of the difference between continuousand semidiscrete solutions by quantities that can be calculatedfrom the approximation and given data. 相似文献
4.
In this paper we consider the numerical approximation of steady and unsteady generalized Newtonian fluid flows using divergence free finite elements generated by the Powell–Sabin–Heindl elements. We derive a priori and a posteriori finite element error estimates and prove convergence of the method of successive approximations for the steady flow case. A priori error estimates of unsteady flows are also considered. These results provide a theoretical foundation and supporting numerical studies are to be provided in Part II. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
5.
Gabriel N. Gatica Ernst P. Stephan 《Numerical Methods for Partial Differential Equations》2002,18(1):105-128
This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babu?ka‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002 相似文献
6.
Recently, molecular imaging has been rapidly developed to studyphysiological and pathological processes in vivo at the cellularand molecular levels. Among molecular imaging modalities, opticalimaging has attracted a major attention for its unique advantages.In this paper, we establish a mathematical framework for multispectralbioluminescence tomography (BLT) that allows simultaneous studiesof multiple optical reporters. We show solution existence, uniquenessand continuous dependence on data as well as the limiting behaviourswhen the regularization parameter approaches zero or when thepenalty parameter approaches infinity. Then, we propose twonumerical schemes for multispectral BLT and derive error estimatesfor the corresponding solutions. 相似文献
7.
Boris Andreianov Franck Boyer Florence Hubert 《Numerical Methods for Partial Differential Equations》2007,23(1):145-195
Discrete duality finite volume schemes on general meshes, introduced by Hermeline and Domelevo and Omnès for the Laplace equation, are proposed for nonlinear diffusion problems in 2D with nonhomogeneous Dirichlet boundary condition. This approach allows the discretization of non linear fluxes in such a way that the discrete operator inherits the key properties of the continuous one. Furthermore, it is well adapted to very general meshes including the case of nonconformal locally refined meshes. We show that the approximate solution exists and is unique, which is not obvious since the scheme is nonlinear. We prove that, for general W?1,p′(Ω) source term and W1‐(1/p),p(?Ω) boundary data, the approximate solution and its discrete gradient converge strongly towards the exact solution and its gradient, respectively, in appropriate Lebesgue spaces. Finally, error estimates are given in the case where the solution is assumed to be in W2,p(Ω). Numerical examples are given, including those on locally refined meshes. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
8.
The paper deals with a singularly perturbed reaction diffusionmodel problem. The focus is on reliable a posteriori error estimatorsfor the H1 seminorm that can be applied to anisotropic finiteelement meshes. A residual error estimator and a local problemerror estimator are proposed and rigorously analysed. They arelocally equivalent, and both bound the error reliably. Threemodifications of these estimators are introduced and discussed. Much attention is given to the performance of the error estimatorin numerical experiments. This helps to identify those estimatorsthat are suitable for practical applications. 相似文献
9.
It follows from an analysis of the error levels of TG evaluation methods that it is a conceptual error to disregard the analogies
of mass, energy and momentum streams of subordinate partial processes. This error is bypassed by means of the introduced method
of dimensionless analysis and by determining the characteristic, constants-like data of thermal processes by using the measured
data directly. These methods are very suitable for increasing the consistency of the calculated results by seeking for similarity,
even in comparisons of measurements made under very different conditions and for emphasizing the differences too, quantitatively.
With this new interpretation of TG processes, the idea of the kinetic compensation effect becomes only a consequence of the
discussed conceptual error.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
10.
We consider a binary classification problem for a test sequence to determine from which source the sequence is generated. The system classifies the test sequence based on empirically observed (training) sequences obtained from unknown sources and . We analyze the asymptotic fundamental limits of statistical classification for sources with multiple subclasses. We investigate the first- and second-order maximum error exponents under the constraint that the type-I error probability for all pairs of distributions decays exponentially fast and the type-II error probability is upper bounded by a small constant. In this paper, we first give a classifier which achieves the asymptotically maximum error exponent in the class of deterministic classifiers for sources with multiple subclasses, and then provide a characterization of the first-order error exponent. We next provide a characterization of the second-order error exponent in the case where only has multiple subclasses but does not. We generalize our results to classification in the case that and are a stationary and memoryless source and a mixed memoryless source with general mixture, respectively. 相似文献