ERROR ANALYSIS FOR FINITE-ELEMENT METHODS FOR STEADY NATURAL-CONVECTION PROBLEMS
ERROR ANALYSIS FOR FINITE-ELEMENT METHODS FOR STEADY NATURAL-CONVECTION PROBLEMS
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DOI：
10.1080/01630569008816383
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发表时间：
1990-01-01
影响因子：
1.2
通讯作者：
LAYTON, W
中科院分区：
文献类型：
--
作者：
BOLAND, J;LAYTON, W
我们分析了有限元法在近似所谓自由对流或自然对流问题时的误差。我们还在分析中考虑了传导固体壁的影响。在Rayleigh数和Prandtl数的唯一性条件下，我们给出了流体变量的“潜稳”有限元空间和温度变量的一般符合有限元空间的直接、准最优误差估计。在较大的瑞利数下，我们给出了类似的，渐近误差估计，基于我们也建立的真解（upT）的局部唯一性的分析。
We analyze the error in finite element methods in approximating, so-called, free or natural convection problems. We also include the effects of conducting solid walls in our analysis. Under a uniqueness condition on the Rayleigh and Prandtl numbers (which we derive), we give direct, quasioptimal error estimates for “div-stable” finite element spaces for the fluid variables and general conforming finite element spaces for the temperature. At larger Rayleigh numbers, we give analogous, asymptotic error estimates, basing this analysis upon local uniqueness properties of the true solution (upT), which we also establish.