A posteriori error estimates for the Richards equation


A posteriori error estimator as a function of the final time (left), the corresponding effectivity index (right)

Main results:

  • nonlinear advection–reaction–diffusion equation;
  • parabolic–hyperbolic and parabolic–elliptic degeneracies;
  • a posteriori error estimates:
    • guaranteed upper bound in nonlocal-in-time (time-integrated) norms;
    • local space–time efficiency in standard norms;
  • the reliability and efficiency norms coincide when there is no nonlinearity;
  • distinction of error components.

Details: preprint with Koondanibha Mitra

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