Unconditionally Convergent $L1$-Galerkin FEMs for Nonlinear Time-Fractional Schrödinger Equations

Volume: 39, Issue: 6, Pages: A3067 - A3088
Published: Jan 1, 2017
Abstract
In this paper, a linearized L1Galerkin finite element method is proposed to solve the multidimensional nonlinear time-fractional Schrödinger equation. In terms of a temporal-spatial error splitting argument, we prove that the finite element approximations in the L^2norm and L^\inftynorm are bounded without any time-step size conditions. More importantly, by using a discrete fractional Gronwall-type inequality, optimal error estimates of...
Paper Details
Title
Unconditionally Convergent $L1$-Galerkin FEMs for Nonlinear Time-Fractional Schrödinger Equations
Published Date
Jan 1, 2017
Volume
39
Issue
6
Pages
A3067 - A3088
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