We prove that the error estimates of a large class of nonconforming finite elements are dominated by their approximation errors, which means that the well-known Cea’s lemma is still valid for these nonconforming fini...
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We prove that the error estimates of a large class of nonconforming finite elements are dominated by their approximation errors, which means that the well-known Cea’s lemma is still valid for these nonconforming finite element methods. Furthermore, we derive the error estimates in both energy and L2 norms under the regularity assumption u ∈ H1+s(Ω) with any s > 0. The extensions to other related problems are possible.
The two-sided rank-one (TR1) update method was introduced by Griewank and Walther (2002) for solving nonlinear equations. It generates dense approximations of the Jacobian and thus is not applicable to large-scale spa...
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The two-sided rank-one (TR1) update method was introduced by Griewank and Walther (2002) for solving nonlinear equations. It generates dense approximations of the Jacobian and thus is not applicable to large-scale sparse problems. To overcome this difficulty, we propose sparse extensions of the TR1 update and give some convergence analysis. The numerical experiments show that some of our extensions are superior to the TR1 update method. Some convergence analysis is also presented.
The understanding of biological processes, e.g. related to cardio-vascular disease and treatment, can significantly be improved by numerical simulation. In this paper, we present an approach for a multiscale simulatio...
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The understanding of biological processes, e.g. related to cardio-vascular disease and treatment, can significantly be improved by numerical simulation. In this paper, we present an approach for a multiscale simulation environment, applied for the prediction of in-stent re-stenos is. Our focus is on the coupling of distributed, heterogeneous hardware to take into account the different requirements of the coupled sub-systems concerning computing power. For such a concept, which is an extension of the standard multiscale computing approach, we want to apply the term Distributed Multiscale computing.
作者：
Kong LinghuaHong JialinZhang JingjingSchool of Mathematics and Information Science
Jiangxi Normal UniversityNanchang Jiangxi 330022 China Institute of Computational Mathematics and Scientific/Engineering Computing AMSS CAS P.O.Box 2719 Beijing 100190 China School of Mathematics and Information Science Henan Polytechnic University Jiaozuo Henan 454000 China
The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplecticFourier spectral (MSFS) methods will be employed to solve the fourth-orderSchrodinger equations with trapped term. Using the idea of split-step numer...
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The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplecticFourier spectral (MSFS) methods will be employed to solve the fourth-orderSchrodinger equations with trapped term. Using the idea of split-step numericalmethod and the MSRK methods, we devise a new kind of multi-symplectic integrators, which is called split-step multi-symplectic (SSMS) methods. The numerical experiments show that the proposed SSMS methods are more efficient than the conventionalmulti-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties.
The Burgers＇ equation with uncertain initial and boundary conditions is approximated using a Polynomial Chaos Expansion （PCE） approach where the solution is represented as a series of stochastic, orthogonal polynom...
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The Burgers＇ equation with uncertain initial and boundary conditions is approximated using a Polynomial Chaos Expansion （PCE） approach where the solution is represented as a series of stochastic, orthogonal polynomials. The resulting truncated PCE system is solved using a novel numerical discretization method based on spatial derivative operators satisfying the summation by parts property and weak boundary conditions to ensure stability. The resulting PCE solution yields an accurate quantitative description of the stochastic evolution of the system, provided that appropriate boundary conditions are available. The specification of the boundary data is shown to influence the solution; we will discuss the problematic implications of the lack of precisely characterized boundary data and possible ways of imposing stable and accurate boundary conditions.
Fast facial points fitting plays an important role in applications such as Human-Computer Interaction, entertainment, surveillance, and is highly relevant to the techniques of facial expression analysis, face recognit...
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In this paper, we present a new flexible alignment method to align two or more similar images. By minimizing an energy functional measuring the difference of the initial image and target image, a L2-gradient flow is d...
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We present a numerical study of the energy spectra and fluxes in the inertial range of turbulent Rayleigh-Bénard convection for a wide range of Prandtl number. We consider both free-slip and no-slip conditions fo...
We present a numerical study of the energy spectra and fluxes in the inertial range of turbulent Rayleigh-Bénard convection for a wide range of Prandtl number. We consider both free-slip and no-slip conditions for our simulation. Our results support the Kolmogorov-Obukhov (KO) scaling for velocity field for zero-Prandtl number and low-Prandtl number (P 1) convection. For large Prandtl number (P > 1) convection, the Bolgiano-Obukhov scaling (BO) appears to agree with the numerical results better than the KO scaling. We provide phenomenological arguments for the zero-Prandtl and low-Prandtl number convection.
In this paper, we study the finite element method for a nonsmooth elliptic equation. Error analysis is presented, including a priori and a posteriori error estimates as well as superconvergence analysis. We also propo...
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In this paper, we study the finite element method for a nonsmooth elliptic equation. Error analysis is presented, including a priori and a posteriori error estimates as well as superconvergence analysis. We also propose two algorithms for solving the underlying equation. Numerical experiments are employed to confirm our error estimations and the efficiency of our algorithms.
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