球面 Whittle–Matérn 高斯随机场的曲面有限元逼近
Surface finite element approximation of spherical Whittle--Matérn Gaussian random fields
AI总结：
本文研究球面 Whittle–Matérn 高斯随机场的曲面有限元逼近，结合递归格式与 Dunford–Taylor 积分求积处理分数阶算子，并给出强误差分析和计算复杂度上界。
摘要：
球面 Whittle–Matérn 高斯随机场被视为球面上分数阶椭圆型随机偏微分方程的解。逼近采用曲面有限元方法。算子的非分数阶部分通过递归格式求解，而分数阶部分则利用 Dunford–Taylor 积分表示的求积公式进行处理。文中进行了强误差分析，并根据精度对计算复杂度给出了上界。针对不同参数选择的数值实验验证了理论结果。
英文摘要：
Spherical Whittle--Matérn Gaussian random fields are considered as solutions to fractional elliptic stochastic partial differential equations on the sphere. Approximation is done with surface finite elements. While the non-fractional part of the operator is solved by a recursive scheme, a quadrature of the Dunford--Taylor integral representation is employed for the fractional part. Strong error analysis is performed, and the computational complexity is bounded in terms of the accuracy. Numerical experiments for different choices of parameters confirm the theoretical findings.
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