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Structure‐preserving Galerkin approximation for a class of nonlinear port‐Hamiltonian partial differential equations on networks
Author(s) -
Liljegren-Sailer Björn,
Marheineke Nicole
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900399
Subject(s) - nonlinear system , galerkin method , partial differential equation , mathematics , hamiltonian (control theory) , reduction (mathematics) , class (philosophy) , context (archaeology) , mathematical optimization , computer science , mathematical analysis , physics , geometry , artificial intelligence , paleontology , quantum mechanics , biology
The development of structure‐preserving approximation methods, which regard fundamental underlying physical principles, is an active field of research. Especially when the application of model reduction is desirable, systematic and rather generic approaches are of great interest. In this contribution we discuss a structure‐preserving Galerkin approach for a prototypical class of nonlinear partial differential equations on networks. Its derivation is guided by port‐Hamiltonian‐type modeling and appropriate variational principles. Also complexity‐reduction schemes can be integrated in a structure‐preserving way, which becomes crucial in the context of model reduction for nonlinear systems.