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Two-grid discretization techniques for linear and nonlinear PDEs. (English) Zbl 0860.65119
Some discretization technique based on two (or more) finite element subspaces for solving partial differential equations is presented. Convergence estimates are derived to justify the efficiency of these algorithms. Some two-grid methods for nonsymmetric and/or indefinite linear partial differential equations (PDEs) are discussed. The main two-grid and some multigrid algorithms are also presented.

MSC:
65N55Multigrid methods; domain decomposition (BVP of PDE)
65F10Iterative methods for linear systems
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
35J25Second order elliptic equations, boundary value problems
65N12Stability and convergence of numerical methods (BVP of PDE)
35J65Nonlinear boundary value problems for linear elliptic equations