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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:
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
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