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.
CitationSarrate, J.; Peraire, J.; Patera, A. A posteriori finite element error bounds for non-linear outputs of the Helmholtz equation. "International journal for numerical methods in fluids", Setembre 1999, vol. 31, núm. 1, The definitive version is available at http://www3.interscience.wiley.com/journal/64000040/abstract, p. 17-36.
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