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

pol_dist

Adaptive mesh & polynomial-degree distribution

smooth_solution

Smooth solution of a peak form

pol_dist

Exponential convergence for hp-adaptivity

hp

Effectivity index of the guaranteed bound on the error reduction

CPU_times

Speedup of inexact solver

hp

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 with Patrik Daniel, Alexandre Ern, and Iain Smears (preprint), paper with Patrik Daniel and Alexandre Ern (preprint), see also presentation

Comments are closed.