Goal-oriented adaptivity with inexact solvers

goal

Goal error (left), effectivity indices (middle), and number of necessary algebraic solver iterations (right), 10e−8 relative residual precision versus adaptive stopping criteria, 3D vertex singularity

Main results:

  • quantity of interest given by a volumetric (source) or a surface (flux) term;
  • same discretization of both primal and dual problems;
  • inexact algebraic solvers for both primal and dual problems;
  • guaranteed upper bound on the goal error
  • unified framework covering basically any numerical method (conforming, nonconforming, and discontinuous Galerkin finite elements, finite volumes).

Details: paper (preprint) with Gouranga Mallik and Soleiman Yousef

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