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Incremental unknowns on nonuniform meshes. (English) Zbl 0913.65088
Incremental unknowns were introduced to solve nonlinear partial differential equations. This method is extended to non-uniform meshes here in order to be able to solve boundary layer problems as well. The emphasis of this paper is on elliptic differential operators in 1 to 3 dimensions. Specifically second-order incremental unknowns are introduced for the coarse and fine grid components. It is shown that the resulting matrix representation of the thus discretized partial differential equation will have a smaller condition number than the one for the uniform mesh case for several standard problems in computational fluid dynamics.
Reviewer: F.Uhlig (Auburn)

MSC:
65N06 Finite difference methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
76D05 Navier-Stokes equations for incompressible viscous fluids
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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