A new grid-projection method is constructed for solving elliptic problems with a small parameter at highest derivatives on adaptive irregular grids. A direct rather than a variational problem formulation is used. The approximate solution in every cell is a quadratic polynomial. The coefficients of the polynomial are determined from the collocation (least-squares) equations and consistency conditions or boundary conditions. The conditions for linear combinations of the solution and its derivative along the normal to the boundary between the cells to be continuous are the consistency conditions. These conditions are met in the sense of the collocation (least-squares) method. Numerical examples are considered, including a problem with internal layers, for which the method we suggest yields a good uniform accuracy.Brought to you by | University of Arizona Authenticated Download Date | 5/30/15 9:39 PM
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