Kelly-Based h-Adaptivity (02-kelly)

This is yet another version of the example “01-intro” that employs a conventional Kelly-type error estimate to perform h-adaptivity. The Kelly error estimate is based on jumps in solution gradients across element edges, and it does not use the solution-pair approach that Hermes uses by default. Most notable differences compared to “01-intro” are:

Calculating Kelly error estimate

Instead of a reference solution, one calculates an error estimate based on gradient jumps:

// Calculate element errors and total error estimate.
info("Calculating error estimate.");
bool ignore_visited_segments = true;
KellyTypeAdapt<double> adaptivity(&space, ignore_visited_segments,
  USE_EPS_IN_INTERFACE_ESTIMATOR
  ?
  new CustomInterfaceEstimatorScalingFunction("Motor", EPS_MOTOR, "Air", EPS_AIR)
  :
  new CustomInterfaceEstimatorScalingFunction);

adaptivity.add_error_estimator_surf(new
  Hermes::Hermes2D::BasicKellyAdapt<double>::ErrorEstimatorFormKelly());

if (USE_RESIDUAL_ESTIMATOR)
{
  adaptivity.add_error_estimator_vol(new ResidualErrorFormMotor("Motor", EPS_MOTOR));
  adaptivity.add_error_estimator_vol(new ResidualErrorFormAir("Air", EPS_AIR));
}

Normalizing error estimate by energy norm

This is optional:

if (USE_EPS_IN_INTERFACE_ESTIMATOR)
  // Use normalization by energy norm.
  adaptivity.set_error_form(new EnergyErrorForm(&wf));

The rest of the adaptivity loop is as usual.