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Support elemental Exodus output for higher-order discontinuous (non-CONSTANT) variables #4562

Description

@kyriv-lab

Resolves idaholab/moose#31427.

MOOSE's Exodus output of higher-order (order > 0) discontinuous MONOMIAL variables currently falls back to nodal output, which averages values across neighboring elements and smears sharp features (e.g. at subdomain interfaces).

The blocker is on the libMesh side:

  • EquationSystems::is_elemental_data_fe_type() only accepts CONSTANT order.
  • EquationSystems::build_parallel_elemental_solution_vector() copies a single DOF per component, which is only valid for CONSTANT order.
  • ExodusII_IO::write_element_data() has no way to opt into elemental output for these variables.

The fix should be opt-in only, since existing exodiff-based regression tests depend on the current default behavior.

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