Paper Info
Title
Mixed and least-squares finite element methods with application to linear hyperbolic problems.
Abstract
In this paper, a few dual least-squares finite element methods and their application to scalar linear hyperbolic problems are studied. The purpose is to obtain L-2-norm approximations on finite element spaces of the exact solutions to hyperbolic partial differential equations of interest. This is approached by approximating the generally infeasible quadratic minimization that defines the L-2-orthogonal projection of the exact solution, by feasible least-squares principles using the ideas of the original.. LL* method proposed in the context of elliptic equations. All methods in this paper are founded upon and extend the LL* approach that is rather general and applicable beyond the setting of elliptic problems. Error bounds are shown that point to the factors affecting the convergence and provide conditions that guarantee optimal rates. Furthermore, the preconditioning of the resulting linear systems is discussed. Numerical results are provided to illustrate the behavior of the methods on common finite element spaces.
Year
DOI
Venue
2018
10.1002/nla.2150
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
Keywords
DocType
Volume
block preconditioners,discontinuous coefficients,dual methods,exponential layers,finite element methods,first-order hyperbolic problems,least-squares methods,negative-norm methods
Journal
25.0
Issue
ISSN
Citations 
SP3.0
1070-5325
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
D. Kalchev141.80
Thomas A. Manteuffel234953.64
Steffen Münzenmaier3122.74