Polytopal meshes and complex porous media flows

black oil

Gas saturation (left) and a posteriori error estimates (right) for the black-oil model on general polytopal meshes

stopping criteria

Adaptive stopping criteria for the linear solver

gain

Gain factor when using linear solver and space mesh adaptivity (no nonlinear solver and time step adaptivity)

Main results:

  • general polytopal meshes;
  • easy-to-implement and fast-to-run a posteriori error estimates given by a simple matrix–vector multiplication;
  • works for any lowest-order locally conservative method;
  • guaranteed upper bound on the total error;
  • distinction of different error components (spatial discretization, temporal discretization, linearization, algebraic solver);
  • unsteady nonlinear coupled degenerate problems (multiphase multicomponent flows in porous media).

Details: paper with Soleiman Yousef (preprint) and presentation

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