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An accuracy analysis of mass matrix lumping for three‐dimensional, unsaturated flow, finite element, porous media computations using analytical solutions
Author(s) -
Tracy Fred T.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700165
Subject(s) - finite element method , porous medium , matrix (chemical analysis) , convergence (economics) , mass matrix , flow (mathematics) , transient (computer programming) , galerkin method , mathematics , computation , vadose zone , nonlinear system , groundwater , mechanics , mathematical analysis , porosity , computer science , geotechnical engineering , physics , algorithm , engineering , geometry , chemistry , thermodynamics , chromatography , economic growth , operating system , quantum mechanics , nuclear physics , neutrino , economics
Lumping of the mass matrix for transient problems is the state of the practice for finite element groundwater programs. This improves nonlinear convergence where there is unsaturated flow, but the discovery was made that the accuracy of the results is reduced significantly for a test problem. This paper compares results from a recently derived transient three‐dimensional (3‐D) analytical solution for a given unsaturated flow test problem with those obtained from a standard parallel Galerkin 3‐D finite element groundwater program with the mass matrix lumping option turned both on and off. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)