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Adjoint Error Estimation for a Pseudo‐Spectral Approach to Stochastic Field‐Circuit Coupled Problems
Author(s) -
Römer Ulrich,
Schöps Sebastian
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510345
Subject(s) - estimator , polynomial , collocation (remote sensing) , degree (music) , mathematics , field (mathematics) , degree of a polynomial , stochastic differential equation , collation , algebraic number , algebraic equation , work (physics) , collocation method , differential equation , computer science , ordinary differential equation , mathematical analysis , nonlinear system , pure mathematics , statistics , mechanical engineering , engineering , physics , quantum mechanics , machine learning , acoustics , operating system
This work is concerned with the numerical approximation of random differential‐algebraic equations (DAE), arising from electric field‐circuit coupled problems. Using the adjoint DAE, the stochastic collation error is analyzed. The error can be evaluated using a collocation method of the same polynomial degree for the adjoint DAE. In particular, there is no need for constructing a solution of higher polynomial degree. The accuracy of the estimator is illustrated by a numerical example. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)