Abstract
AbstractThe 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.
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