论文标题
半线性时间分数扩散问题的galerkin型方法
Galerkin Type Methods for Semilinear Time-Fractional Diffusion Problems
论文作者
论文摘要
对于具有平稳且非平滑初始数据的情况，我们得出了涉及Caputo衍生品的半线性时间折段量次扩散问题的最佳$ l^2 $ -Error估计。引入了一个通用框架，允许对盖尔金型空间近似方法进行统一的误差分析。该分析基于半群类型方法，并利用相关椭圆操作员逆的属性。及时使用向后的Euler卷积正交方法，在同一框架中分析了完全离散的方案。提出了包括构象，不合格和混合有限元（FE）方法在内的数值示例，以说明理论结果。
We derive optimal $L^2$-error estimates for semilinear time-fractional subdiffusion problems involving Caputo derivatives in time of order $α\in (0,1)$, for cases with smooth and nonsmooth initial data. A general framework is introduced allowing a unified error analysis of Galerkin type space approximation methods. The analysis is based on a semigroup type approach and exploits the properties of the inverse of the associated elliptic operator. Completely discrete schemes are analyzed in the same framework using a backward Euler convolution quadrature method in time. Numerical examples including conforming, nonconforming and mixed finite element (FE) methods are presented to illustrate the theoretical results.
