论文标题
对数正态问题的递归第一瞬间方程的规律性和稀疏近似
Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem
论文作者
论文摘要
我们使用对数正态渗透性场研究达西边界价值问题。我们采用了一种扰动方法，在泰勒系列围绕该系数的名义值中扩展了解决方案，并通过其Taylor多项式的预期值近似PDE的随机解决方案的期望值。由泰勒多项式（第一矩方程）的预期值满足的递归确定性方程是正式得出的。事实证明，递归的适合性和规律性结果在具有混合规律性的Sobolev太空值Hölder空间中保持。然后，通过稀疏近似技术将递归的第一瞬间方程离散，并得出收敛速率。
We study the Darcy boundary value problem with log-normal permeability field. We adopt a perturbation approach, expanding the solution in Taylor series around the nominal value of the coefficient, and approximating the expected value of the stochastic solution of the PDE by the expected value of its Taylor polynomial. The recursive deterministic equation satisfied by the expected value of the Taylor polynomial (first moment equation) is formally derived. Well-posedness and regularity results for the recursion are proved to hold in Sobolev space-valued Hölder spaces with mixed regularity. The recursive first moment equation is then discretized by means of a sparse approximation technique, and the convergence rates are derived.
