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Least squares collocation solution of differential equations on irregularly shaped domains using orthogonal meshes
Author(s) -
Laible J. P.,
Pinder G. F.
Publication year - 1989
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.1690050406
Subject(s) - mathematics , orthogonal collocation , collocation (remote sensing) , collocation method , boundary value problem , convergence (economics) , least squares function approximation , rate of convergence , polygon mesh , mathematical analysis , differential equation , ordinary differential equation , geometry , computer science , estimator , key (lock) , statistics , computer security , machine learning , economic growth , economics
The least squares collocation (LESCO) method has been formulated to solve differential equations defined over irregular domains using a more convenient orthogonal computational mesh. The LESCO method is described in detail for second‐order boundary value problems and applied to the time‐dependent diffusion and advection‐diffusion equations defined over two‐dimensional irregular domains. Particular attention is given to the proper procedure for applying boundary conditions. Accuracy, convergence, and consistency are examined. For cubic elements with arbitrary location of collocation points, the convergence rate is between 3rd and 4th order. The major advantages of this method are reduced input data requirements, a more robust procedure for forming the equations, positive definite matrices, and flexibility in distrbuting errors.