
Equivalence between a timefractional and an integerorder gradient flow: The memory effect reflected in the energy
Timefractional partial differential equations are nonlocal in time and ...
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Energydissipation for timefractional phasefield equations
We consider a class of timefractional phase field models including the ...
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Pointwiseintime a posteriori error control for timefractional parabolic equations
For timefractional parabolic equations with a Caputo time derivative of...
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Numerical Energy Dissipation for TimeFractional PhaseField Equations
The energy dissipation is an important and essential property of classic...
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Optimal error estimate of a conservative Fourier pseudospectral method for the space fractional nonlinear Schrödinger equation
In this paper, we consider the error analysis of a conservative Fourier ...
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An a posteriori error estimate of the outer normal derivative using dual weights
We derive a residual based aposteriori error estimate for the outer nor...
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Time fractional gradient flows: Theory and numerics
We develop the theory of fractional gradient flows: an evolution aimed at the minimization of a convex, l.s.c. energy, with memory effects. This memory is characterized by the fact that the negative of the (sub)gradient of the energy equals the socalled Caputo derivative of the state. We introduce the notion of energy solutions, for which we provide existence, uniqueness and certain regularizing effects. We also consider Lipschitz perturbations of this energy. For these problems we provide an a posteriori error estimate and show its reliability. This estimate depends only on the problem data, and imposes no constraints between consecutive timesteps. On the basis of this estimate we provide an a priori error analysis that makes no assumptions on the smoothness of the solution.
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