957 research outputs found
Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales: proofs
We consider a coupled system of two singularly perturbed reaction-diffusion
equations, with two small parameters , each
multiplying the highest derivative in the equations. The presence of these
parameters causes the solution(s) to have \emph{boundary layers} which overlap
and interact, based on the relative size of and . We
construct full asymptotic expansions together with error bounds that cover the
complete range . For the present case of analytic
input data, we derive derivative growth estimates for the terms of the
asymptotic expansion that are explicit in the perturbation parameters and the
expansion order
Local convergence of the FEM for the integral fractional Laplacian
We provide for first order discretizations of the integral fractional
Laplacian sharp local error estimates on proper subdomains in both the local
-norm and the localized energy norm. Our estimates have the form of a
local best approximation error plus a global error measured in a weaker norm
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