Least‐squares finite element method and preconditioned conjugate gradient solution
- 1 July 1987
- journal article
- research article
- Published by Wiley in International Journal for Numerical Methods in Engineering
- Vol. 24 (7) , 1283-1296
- https://doi.org/10.1002/nme.1620240705
Abstract
A least‐squares variational procedure for first‐order systems of differential equations and an approximate formulation based on finite elements are developed. Error estimates, a condition number bound and analysis of weighting factors are given. Steepest descent and conjugate gradient solution procedures are examined, and an appropriate preconditioner constructed which is demonstrated to yield rapid convergence and to be insensitive to problem size. Numerical studies of rates of convergence for a test problem are given.Keywords
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