Local space-time efficiency

meshes

Mesh coarsening and refinement treated by local problems on a common submesh

Main results (heat equation):

  • inf-sup equality with constant 1;
  • any order conforming continuous Galerkin in space;
  • any order discontinuous Galerkin in time;
  • guranteed reliability (upper bound);
  • efficiency local with respect to both space and time;
  • robustness with respect to polynomial degrees both in space and time;
  • arbitrary space mesh refinement and coarsening between time steps (no transition condition);
  • equivalence between global and local norms.

Details: paper with Alexandre Ern and Iain Smears and presentation; see also paper in the energy norm setting (preprint)

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