On the Finite Volume Element Method for General Self-Adjoint Elliptic Problems
On the Finite Volume Element Method for General Self-Adjoint Elliptic Problems
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DOI：
10.1137/s0036142994264699
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发表时间：
1998-10
影响因子：
2.9
通讯作者：
Jianguo Huang;Shitong Xi
中科院分区：
文献类型：
--
作者：
Jianguo Huang;Shitong Xi
有限体积元法是一种求解偏微分方程的离散化方法。本文研究了基于三角剖分的一般自伴随椭圆边值问题的离散化能量误差估计，在该问题上存在线性有限元空间和一类非常一般的控制体积（协体积）。本文的能量误差估计也是最优的，但[R]中给出的协体积的限制条件。E. Bank， D. J. Rose, SIAM J. number。分析的。， 24 (1987), pp. 777—787],[Z]。蔡问，数字。数学。， 58(1991)，第713—735页]。作者最后提供了一个反例来证明通常意义上期望的l2误差估计并不存在。我们推测在一般情况下$\|u-u_h\|_{0,\Omega}$的最优阶数应为O(h)。
The finite volume element method (FVE) is a discretization technique for partial differential equations. This paper develops discretization energy error estimates for general self-adjoint elliptic boundary value problems with FVE based on triangulations, on which there exist linear finite element spaces, and a very general type of control volumes (covolumes). The energy error estimates of this paper are also optimal but the restriction conditions for the covolumes given in [R. E. Bank and D. J. Rose, SIAM J. Numer. Anal., 24 (1987), pp. 777--787], [Z. Q. Cai, Numer. Math., 58 (1991), pp. 713--735] are removed. The authors finally provide a counterexample to show that an expected L2-error estimate does not exist in the usual sense. It is conjectured that the optimal order of $\|u-u_h\|_{0,\Omega}$ should be O(h) for the general case.