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A posteriori finite element error bounds for non‐linear outputs of the Helmholtz equation
Author(s) -
Sarrate J.,
Peraire J.,
Patera A.
Publication year - 1999
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19990915)31:1<17::aid-fld953>3.0.co;2-x
Subject(s) - helmholtz equation , mathematics , helmholtz free energy , finite element method , a priori and a posteriori , extension (predicate logic) , mathematical analysis , boundary (topology) , domain (mathematical analysis) , boundary element method , upper and lower bounds , boundary value problem , computer science , physics , philosophy , epistemology , thermodynamics , quantum mechanics , programming language
A Neumann subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, constant‐free upper and lower bounds for non‐linear outputs of the Helmholtz equation in two‐dimensional exterior domains is presented. The bound procedure is firstly formulated, with particular emphasis on appropriate extension to complex‐valued equations; then, illustrative numerical examples for outputs, such as the intensity of the scattered wave over a small segment of the domain boundary, are provided. Copyright © 1999 John Wiley & Sons, Ltd.