Convergence of the multigrid $V$-cycle algorithm for second-order boundary value problems without full elliptic regularity
Copyright policy )Convergence of the multigrid $V$-cycle algorithm for second-order boundary value problems without full elliptic regularity
The author considers a second order elliptic boundary value problem (Dirichlet) on some 2D polygonal domains with reentrant corners. For such problems, she analyses the effect of the lack of domain regularity on the asymptotic behavior of the contraction number of a \(V\)-cycle multigrid algorithm with respect to the number of smoothing steps. It is shown that the contraction number uniformly improves with the increase of the number of smoothing steps.
- University of South Carolina United States
- University of South Carolina System United States
domain regularity, second order elliptic boundary value problems, Multigrid methods; domain decomposition for boundary value problems involving PDEs, convergence, Boundary value problems for second-order elliptic equations, finite element method, Stability and convergence of numerical methods for boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Richardson relaxation scheme, multigrid \(V\)-cycle algorithm
domain regularity, second order elliptic boundary value problems, Multigrid methods; domain decomposition for boundary value problems involving PDEs, convergence, Boundary value problems for second-order elliptic equations, finite element method, Stability and convergence of numerical methods for boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Richardson relaxation scheme, multigrid \(V\)-cycle algorithm
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