Potential and flux reconstructions a posteriori error estimates

SIPG

Asymptotic exactness for smooth Laplace solution, SIP discontinuous Galerkin method

hp_conv_E_3

Effectivity indices for hp-adaptivity with hanging nodes, IIP discontinuous Galerkin method

hp_conv_E_1

Exponential convergence for hp-adaptivity with hanging nodes, IIP discontinuous Galerkin method

Main results:

  • potential and equilibrated flux reconstruction estimates in a unified framework;
  • inhomogeneous Dirichlet and Neumann boundary conditions;
  • spatially varying polynomial degree;
  • mixed rectangular-triangular grids;
  • combination with the H(div)-liftings paper: robustness with respect to the number of hanging nodes;
  • asymptotic exactness observed for smooth solutions;
  • hp-adaptivity strategy numerically leading to exponential convergence even for singular solutions.

Details: paper with Vít Dolejší and Alexandre Ern and presentation

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