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A least‐squares method for solving the mixed form of the groundwater flow equations
Author(s) -
Bentley L. R.,
Pinder G. F.
Publication year - 1992
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650140606
Subject(s) - mathematics , method of mean weighted residuals , polygon mesh , least squares function approximation , boundary value problem , finite element method , boundary (topology) , collocation (remote sensing) , estimator , mathematical analysis , mathematical optimization , geometry , galerkin method , computer science , statistics , physics , machine learning , thermodynamics
The mixed form of the areal groundwater flow equations is solved with a least‐squares finite element procedure (LESFEM). Hydraulic head and x ‐ and y ‐directed fluxes are state variables. Physical parameters and state variables are approximated using a bilinear basis. Grid refinements and irregular domain boundaries are implemented on rectangular meshes. Residuals are constructed at collocation points for conservation of mass and Darcy's law. Boundary condition residuals are constructed at discrete points along the boundary. The residuals are weighted, squared and summed. A set of algebraic equations is formed by taking the derivatives of the weighted sum of the squares of the residuals with respect to each unknown parameter in the approximation for the state variable and setting them to zero. Proper choice of a potential scaling parameter and residual weights is essential for the effective application of the algorithm. Test problem results demonstrate that the method is effective for both transient and steady state cases. The LESFEM algorithm generates a C °‐continuous velocity field. The continuous velocity field and the rectangular mesh simplify the implementation of algorithms that require tracking. In addition, rectangular meshes simplify mesh and boundary generation.