Covolume-upwind finite volume approximations for linear elliptic partial differential equations

Ju L.; Tian L.; Xiao X.; Zhao W.

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Covolume-upwind finite volume approximations for linear elliptic partial differential equations

机译：线性椭圆型偏微分方程的迎风向上有限体积近似

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In this paper, we study covolume-upwind finite volume methods on rectangular meshes for solving linear elliptic partial differential equations with mixed boundary conditions. To avoid non-physical numerical oscillations for convection-dominated problems, nonstandard control volumes (covolumes) are generated based on local Peclet's numbers and the upwind principle for finite volume approximations. Two types of discretization schemes with mass lumping are developed with use of bilinear or biquadratic basis functions as the trial space respectively. Some stability analyses of the schemes are presented for the model problem with constant coefficients. Various examples are also carried out to numerically demonstrate stability and optimal convergence of the proposed methods.

机译：在本文中，我们研究了矩形网格上的迎风迎风有限体积方法，用于求解带有混合边界条件的线性椭圆型偏微分方程。为了避免对流主导问题的非物理数值振荡，基于局部Peclet数和有限体积近似的逆风原理生成非标准控制体积（共体积）。分别使用双线性或双二次基函数作为试验空间，开发了两种具有质量集总的离散化方案。针对具有恒定系数的模型问题，给出了该方案的一些稳定性分析。还进行了各种示例，以数值方式证明了所提出方法的稳定性和最佳收敛性。

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《Journal of Computational Physics》 |2012年第18期|共24页
作者
Ju L.; Tian L.; Xiao X.; Zhao W.;
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正文语种 eng
中图分类数学物理方法;
关键词
Convection-dominated; Finite volume approximations; Nonstandard control volumes; Upwind control volumes;

机译：对流为主;有限体积近似;非标准控制体积;迎风控制体积;

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专利

1. Covolume-upwind finite volume approximations for linear elliptic partial differential equations [J] . Ju L., Tian L., Xiao X., Journal of Computational Physics . 2012,第18期

机译：线性椭圆型偏微分方程的迎风向上有限体积近似
2. SOME A PRIORI ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS OF ELLIPTIC AND PARABOLIC LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS [J] . Christophe Audouze, Prasanth B. Nair International journal for uncertainty quantifications . 2014,第5期

机译：椭圆和抛物线型线性随机偏微分方程的有限元逼近的一些先验误差估计
3. The finite element approximation of semilinear elliptic partial differential equations with critical exponents in the cube [J] . C. J. Budd, A. R. Humphries, A. J. Wathen SIAM Journal on Scientific Computing . 1999,第5期

机译：立方中具有临界指数的半线性椭圆型偏微分方程的有限元逼近。
4. A Posteriori Error Bounds for Reduced- Basis Approximation of Parametrized Noncoercive and Nonlinear Elliptic Partial Differential Equations [C] . K. Veroy, C. Prud, D. Rovas, AIAA Computational Fluid Dynamics Conference . 2003

机译：参数化非矫顽和非线性椭圆型偏微分方程的简化基近似的后验误差界
5. Study on Covolume-Upwind Finite Volume Approximations for Linear Parabolic Partial Differential Equations. [D] . Tatano, Rosalia. 2013

机译：线性抛物型偏微分方程的迎风迎风有限体积近似研究。
6. High accuracy finite difference approximation to solutions of elliptic partial differential equations [O] . Robert E. Lynch, John R. Rice 1978

机译：椭圆型偏微分方程解的高精度有限差分近似
7. THE FINITE ELEMENT APPROXIMATION OF SEMILINEAR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS WITH CRITICAL EXPONENTS IN THE CUBE [O] . C. J. Buddy, A. R. Humphriesz, A. J. Wathenx 2015

机译：CUBE中具有临界指数的半线性椭圆型偏微分方程的有限元逼近
8. Some Results of Existence and Uniqueness for Nonlinear Partial Differential Equations and Remarks on the Approximation of Some Nonlinear Elliptic Equations [R] . Temam, R. 1968

机译：非线性偏微分方程存在唯一性的若干结果及若干非线性椭圆型方程的逼近

Covolume-upwind finite volume approximations for linear elliptic partial differential equations

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