空间离散次扩散Fokker-Planck方程的一致稳定性
Uniform stability for a spatially-discrete, subdiffusive Fokker-Planck equation
摘要：
证明了分数阶Fokker-Planck方程的空间离散Galerkin解的稳定性估计，在几个方面改进了以前的结果。我们的主要目标是建立的稳定常数是有界的分数扩散指数$α\in(0,1]$一致。此外，我们占的存在下，一个非齐次项，并显示的Galerkin解决方案的梯度的稳定性估计。作为副产品，标准有限元逼近的误差界的证明被简化。
英文摘要：
We prove stability estimates for the spatially discrete, Galerkin solution of a fractional Fokker-Planck equation, improving on previous results in several respects. Our main goal is to establish that the stability constants are bounded uniformly in the fractional diffusion exponent $α\in(0,1]$. In addition, we account for the presence of an inhomogeneous term and show a stability estimate for the gradient of the Galerkin solution. As a by-product, the proofs of error bounds for a standard finite element approximation are simplified.
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