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Integration of \(hp\)-adaptivity and a two-grid solver for elliptic problems. (English) Zbl 1093.65112
Summary: We present implementation details and analyze convergence of a two-grid solver forming the core of the fully automatic \(hp\)-adaptive strategy for elliptic problems. The solver delivers a solution for a fine grid obtained from an arbitrary coarse \(hp\)-grid by a global \(hp\)-refinement. The classical V-cycle algorithm combines an overlapping block Jacobi smoother with optimal relaxation, and a direct solved on the coarse grid. A simple theoretical analysis is illustrated with extensive numerical experimentation.

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
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
35J25 Boundary value problems for second-order elliptic equations
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