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Some pointwise estimates for the finite element solution of a radial nonlinear Schrödinger equation on a class of nonuniform grids
Author(s) -
Tourigny Yves
Publication year - 1994
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.1690100609
Subject(s) - pointwise , superconvergence , mathematics , discretization , finite element method , nonlinear system , symmetry in biology , grid , mathematical analysis , class (philosophy) , symmetry (geometry) , inverse , geometry , physics , quantum mechanics , artificial intelligence , computer science , thermodynamics
We prove new pointwise estimates for the time‐continuous finite element discretization of a nonlinear Schrödinger equation. The analysis relies on the energy method. A superconvergent estimate of the error gradient is derived and we obtain L ∞ estimates via inverse inequalities. We emphasize the case of radial symmetry where the results improve on previously published L 2 estimates by allowing greater flexibility in the choice of spatial grid. Some numerical results are presented, which confirm our theoretical findings. © 1994 John Wiley & Sons, Inc.