hp-FEM for the fractional heat equation
Keyword(s):
Abstract 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 $.
2015 ◽
Vol 2
(1)
◽
Keyword(s):
2020 ◽
Vol 416
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pp. 109540
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