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A note on the least squares solution of the groundwater flow equation
Author(s) -
Bentley L. R.
Publication year - 1994
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690100408
Subject(s) - mathematics , discretization , finite element method , least squares function approximation , partial differential equation , bilinear interpolation , galerkin method , mathematical analysis , basis function , flow (mathematics) , total least squares , mixed finite element method , convergence (economics) , geometry , algorithm , statistics , physics , estimator , thermodynamics , singular value decomposition , economics , economic growth
The least squares finite element method is a member of the weighted residuals class of numerical methods for solving partial differential equations. The least squares finite element method is applied to the groundwater flow equation. Space is discretized with a C 1 continuous trial function and parameters are approximated with a C 0 bilinear basis. Solutions for problems containing parameters with large localized spatial gradients are characterized by errors that are propagated throughout the entire domain. Second‐order spatial convergence is observed, and extreme mesh refinement is required to match Galerkin and mixed least squares finite element results. Temporal discretization should be kept separate from the least squares spatial discretization. © 1994 John Wiley & Sons, Inc.