We consider a time-dependent problem generated by a nonlocal operator in space. Applying for the spatial discretization a scheme based on |$hp$|-finite elements and a Caffarelli–Silvestre extension we obtain a semidiscrete semigroup. The discretization in time is carried out by using |$hp$|-discontinuous Galerkin based time stepping. We prove exponential convergence for such a method in an abstract framework for the discretization in the spatial domain |$\varOmega $|⁠.

中文翻译：

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hp -FEM对于分数热方程

我们考虑由空间中的非本地运算符生成的时间相关问题。申请空间离散化基于| $ hp $ |的方案 有限元和Caffarelli-Silvestre扩展我们得到一个半离散的半群。时间离散化使用| $ hp $ |进行。-不连续的基于Galerkin的时间步进。我们在空间域| $ \ varOmega $ |⁠的离散化抽象框架中证明了这种方法的指数收敛性。