Guaranteed bounds on the error reduction and hp adaptivity with inexact solvers


Adaptive mesh & polynomial-degree distribution


Smooth solution of a peak form


Exponential convergence for hp-adaptivity


Effectivity index of the guaranteed bound on the error reduction


Speedup of inexact solver


Exponential convergence for hp-adaptivity with exact and inexact solvers

Main results:

  • computable guaranteed bound on the error reduction factor (ratio of the errors between two successive hp refinements);
  • homogeneous Neumann local problems via mixed finite elements to obtain error upper bound;
  • homogeneous Dirichlet local problems via conforming finite elements for hp decision;
  • hp-adaptive strategy with numerically exponential convergence rates;
  • inexact algebraic solver taken into account.

Details: Ph.D. thesis of Patrik Daniel, Ph.D. defense presentation; paper (preprint) with Patrik Daniel, Alexandre Ern, and Iain Smears, paper (preprint) with Patrik Daniel and Alexandre Ern, preprint with Patrik Daniel, see also presentation.

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