A Posteriori Finite Element Error Bounds for Nonlinear Outputs of the Helmholtz Equation

Author (s): Sarrate, J., Peraire, J. and Patera
Journal: International Journal for Numerical Methods in Fluids

Volume: 31, Issue 1
Pages: 17 – 36
Date: 1999

We present a Neumann-subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, constant-free upper and lower bounds for nonlinear outputs of the Helmholtz equation in two-dimensional exterior domains. We first formulate the bound procedure, with particular emphasis on appropriate extension to complex-valued equations; we then provide illustrative numerical examples for outputs such as the intensity of the scattered wave over a small segment of the domain boundary.



@article {1999-IJNMF-SPP,
author = {{S}arrate, {J}. and {P}eraire, {J}. and {P}atera, {A}.},
title = {{A} posteriori finite element error bounds for non-linear outputs of the Helmholtz equation},
journal = {{I}nternational {J}ournal for {N}umerical {M}ethods in {F}luids},
volume = {31},
number = {1},
issn = {1097-0363},
doi = {10.1002/(SICI)1097-0363(19990915)31:1<17::AID-FLD953>3.0.CO;2-X},
pages = {17--36},
year = {1999},