Paper Info
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' 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(h(2p)), 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(h(p)), convergence of the finite-element approximation. Finally, we introduce an abstract framework for analyzing the energy laws of general FOSLS discretizations.
Year
DOI
Venue
2017
10.1007/978-3-319-73441-5_1
Lecture Notes in Computer Science
Field
DocType
Volume
Convergence (routing),Least squares,Physical system,Mathematical analysis,First order system,Expected value,Heat equation,Initial value problem,Law,Partial differential equation,Mathematics
Conference
10665
ISSN
Citations 
PageRank 
0302-9743
0
0.34
References 
Authors
7
4
Name
Order
Citations
PageRank
J. H. Adler15610.02
Ilya Lashuk200.34
S. P. MacLachlan39811.78
Ludmil Zikatanov418925.89