@inproceedings{daffdfe062cc41f7af976faf201e8157,

title = "Discrete energy laws for the first-order system least-squares finite-element approach",

abstract = "This paper analyzes the discrete energy laws associated with first-order system least-squares (FOSLS) discretizations of time-dependent partial differential equations. Using the heat equation and the time-dependent Stokes{\textquoteright} equation as examples, we discuss how accurately a FOSLS finite-element formulation adheres to the underlying energy law associated with the physical system. Using regularity arguments involving the initial condition of the system, we are able to give bounds on the convergence of the discrete energy law to its expected value (zero in the examples presented here). Numerical experiments are performed, showing that the discrete energy laws hold with order O(h2 p), where h is the mesh spacing and p is the order of the finite-element space. Thus, the energy law conformance is held with a higher order than the expected, O(hp), convergence of the finite-element approximation. Finally, we introduce an abstract framework for analyzing the energy laws of general FOSLS discretizations.",

author = "Adler, {J. H.} and I. Lashuk and MacLachlan, {S. P.} and Zikatanov, {L. T.}",

year = "2018",

month = jan,

day = "1",

doi = "10.1007/978-3-319-73441-5_1",

language = "English (US)",

isbn = "9783319734408",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "3--20",

editor = "Ivan Lirkov and Svetozar Margenov",

booktitle = "Large-Scale Scientific Computing - 11th International Conference, LSSC 2017, Revised Selected Papers",

address = "Germany",

note = "11th International Conference on Large-Scale Scientific Computations, LSSC 2017 ; Conference date: 11-09-2017 Through 15-09-2017",

}