An exponentially convergent discretization for space-time fractional parabolic equations using hp-FEM

by   Jens Markus Melenk, et al.

We consider a space-time fractional parabolic problem. Combining a sinc-quadrature based method for discretizing the Riesz-Dunford integral with hp-FEM in space yields an exponentially convergent scheme for the initial boundary value problem with homogeneous right-hand side. For the inhomogeneous problem, an hp-quadrature scheme is implemented. We rigorously prove exponential convergence with focus on small times t, proving robustness with respect to startup singularities due to data incompatibilities.



page 1

page 2

page 3

page 4


Finite Element Analysis of Time Fractional Integro-differential Equations of Kirchhoff type for Non-homogeneous Materials

In this paper, we study an initial-boundary value problem of Kirchhoff t...

The parabolic p-Laplacian with fractional differentiability

We study the parabolic p-Laplacian system in a bounded domain. We deduce...

Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D

We prove weighted analytic regularity for the solution of the integral f...

Exponential Convergence of hp-Time-Stepping in Space-Time Discretizations of Parabolic PDEs

For linear parabolic initial-boundary value problems with self-adjoint, ...

A Space-Time Approach for the Time-Domain Simulation in a Rotating Reference Frame

We approach the discretisation of Maxwell's equations directly in space-...

Optimal error estimate for a space-time discretization for incompressible generalized Newtonian fluids: The Dirichlet problem

In this paper we prove optimal error estimates for solutions with natura...

Galois extensions, positive involutions and an application to unitary space-time coding

We show that under certain conditions every maximal symmetric subfield o...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.