Sharp error estimates of a spectral Galerkin method for a diffusion-reaction equation with integral fractional Laplacian on a disk

2021/03/24 by Zhaopeng Hao, Huiyuan Li, Zhimin Zhang +1 · 2 citations
Mathematics · #Fractional Differential Equations Solutions #Differential Equations and Numerical Methods #Differential Equations and Boundary Problems

paper · doi:10.1090/mcom/3645

Abstract

We investigate a spectral Galerkin method for the two-dimensional fractional diffusion-reaction equations on a disk. We first prove regularity estimates of solutions in the weighted Sobolev space. Then we obtain optimal convergence orders of a spectral Galerkin method for the fractional diffusion-reaction equations in the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L squared"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding="application/x-tex">L²</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and energy norm. We present numerical results to verify the theoretical analysis.

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