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Maximum‐norm a posteriori error bounds for a collocation method applied to a singularly perturbed reaction–diffusion problem in three dimensions
Author(s) -
Radojev Goran,
Linß Torsten
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22414
Subject(s) - mathematics , norm (philosophy) , a priori and a posteriori , collocation method , tensor product , collocation (remote sensing) , dimension (graph theory) , perturbation (astronomy) , singular perturbation , reaction–diffusion system , polygon mesh , mathematical analysis , pure mathematics , geometry , differential equation , ordinary differential equation , computer science , philosophy , physics , epistemology , machine learning , political science , law , quantum mechanics
Abstract Collocation with triquadratic C 1 ‐splines for a singularly perturbed reaction–diffusion problem in three dimension is studied. A posteriori error bound in the maximum norm is derived for the collocation method on arbitrary tensor‐product meshes which is robust in the perturbation parameter. Numerical results are presented that support our theoretical estimate.