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首页> 外文期刊>Differential and integral equations >OPTIMAL RESULTS FOR THE BREZZI-PITKARANTA APPROXIMATION OF VISCOUS FLOW PROBLEMS
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OPTIMAL RESULTS FOR THE BREZZI-PITKARANTA APPROXIMATION OF VISCOUS FLOW PROBLEMS

机译：粘性流问题的BREZZI-PITKARANTA逼近的最佳结果

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摘要

By introducing the term -ε~2Δp into the equation of continuity and an additional Neumann boundary condition for the pressure p, a strongly elliptic system is obtained which is a singular perturbation of the Stokes system. We use parameter-dependent Sobolev norms to derive asymptotically precise estimates for solutions to the perturbed problem as e ε→ 0. This results in optimal estimates for the difference between solutions to both problems; such estimates are not available by the usually applied energy methods. Under additional regularity assumptions for the data, for the energy estimates, the order of convergence with respect to e is improved, and convergence in H~(s+1) and Hs norms is obtained for the velocity and pressure with s ∈ [0,3/2). We verify the asymptotic precision of the estimates by constructing the boundary layers.
机译：通过将-ε〜2Δp项引入连续方程和压力p的附加诺伊曼边界条件中，可以获得强椭圆系统，该系统是Stokes系统的奇异摄动。我们使用与参数有关的Sobolev范数来得出被摄动问题的解的渐近精确估计，即eε→0。此类估算无法通过通常应用的能源方法获得。在数据的其他正则性假设下，对于能量估计，相对于e的收敛阶数得到改善，并且对于s∈[0，的速度和压力，获得了H〜（s + 1）和Hs范数的收敛。 3/2）。我们通过构造边界层来验证估计的渐近精度。

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