{
  "citation": "Harder, Paredes and Valentin (2013), JCP 245, Figure 5, p.117",
  "doi": "10.1016/j.jcp.2013.03.019",
  "python": "3.12.14",
  "numpy": "2.5.3",
  "mesh": "n by n equal squares, each split along its lower-left to upper-right diagonal",
  "abscissa_caveat": "Published h labels are paired with candidate grid spacing 1/n; the candidate geometric macro diameter is sqrt(2)/n. The paper does not specify the exact structured mesh connectivity.",
  "local_space": "RT0/P0 on one triangle per macrocell",
  "formulation": "mixed",
  "trace_degree": 0,
  "boundary_conditions": "zero outward Darcy flux on the whole boundary",
  "pressure_gauge": "integral pressure = 0",
  "assembly_quadrature_order": 10,
  "error_quadrature_order": 12,
  "published_digitization_relative_tolerance": 0.01,
  "quadrature_check": {
    "n": 4,
    "assembly_order": 12,
    "error_order": 14,
    "relative_norm_changes": {
      "rt0_integrated_quadratic_pressure_l2": 1.3322676295501878e-15,
      "flux_l2": 2.220446049250313e-16,
      "macroconstant_pressure_l2": 2.220446049250313e-16,
      "macroconstant_projection_l2": 7.993605777301127e-15
    }
  },
  "comparison_status": "Direct digitized-curve comparison; the exact original mesh and local implementation are not independently confirmed.",
  "results": [
    {
      "n": 4,
      "macro_triangles": 32,
      "grid_spacing": 0.25,
      "macro_diameter": 0.3535533905932738,
      "pressure_l2": 0.2496148257715673,
      "flux_l2": 2.038449406396716,
      "macroconstant_pressure_l2": 0.2496148257715673,
      "macroconstant_projection_l2": 0.05763008915899371,
      "computed_mean": 3.903127820947816e-18,
      "macro_balance_max": 4.440892098500626e-16,
      "algebraic_residual": 1.1393992963329352e-16,
      "rt0_integrated_quadratic_pressure_l2": 0.12253725164198735,
      "flux_l2_relative_difference": -5.88572573558821e-05,
      "macroconstant_pressure_l2_relative_difference": 0.00011762211832655467,
      "macroconstant_projection_l2_relative_difference": -0.00021485616676153452,
      "rt0_integrated_quadratic_pressure_l2_relative_difference": 0.001989908294421694
    },
    {
      "n": 8,
      "macro_triangles": 128,
      "grid_spacing": 0.125,
      "macro_diameter": 0.1767766952966369,
      "pressure_l2": 0.12964984887275863,
      "flux_l2": 1.0131080631609333,
      "macroconstant_pressure_l2": 0.12964984887275868,
      "macroconstant_projection_l2": 0.017837705381970985,
      "computed_mean": -1.4094628242311558e-17,
      "macro_balance_max": 9.159339953157541e-16,
      "algebraic_residual": 2.1224105380197854e-16,
      "rt0_integrated_quadratic_pressure_l2": 0.03170664437100058,
      "flux_l2_relative_difference": 0.0003110656919371735,
      "macroconstant_pressure_l2_relative_difference": -2.975716877362533e-05,
      "macroconstant_projection_l2_relative_difference": -0.00014812592383361967,
      "pressure_l2_eoc": 0.94508310052837,
      "flux_l2_eoc": 1.0086840826849748,
      "macroconstant_pressure_l2_eoc": 0.9450831005283693,
      "macroconstant_projection_l2_eoc": 1.6918922108302086,
      "rt0_integrated_quadratic_pressure_l2_relative_difference": 0.0013547154823827512,
      "rt0_integrated_quadratic_pressure_l2_eoc": 1.9503632939443747
    },
    {
      "n": 16,
      "macro_triangles": 512,
      "grid_spacing": 0.0625,
      "macro_diameter": 0.08838834764831845,
      "pressure_l2": 0.06530540427651137,
      "flux_l2": 0.5044833821741012,
      "macroconstant_pressure_l2": 0.06530540427651138,
      "macroconstant_projection_l2": 0.004704798049362732,
      "computed_mean": -5.963111948670274e-19,
      "macro_balance_max": 9.749145934989656e-16,
      "algebraic_residual": 2.623976915960068e-16,
      "rt0_integrated_quadratic_pressure_l2": 0.007992335075310176,
      "flux_l2_relative_difference": -0.0006014790897890254,
      "macroconstant_pressure_l2_relative_difference": -0.0005908685604870678,
      "macroconstant_projection_l2_relative_difference": -0.0007384765412529193,
      "pressure_l2_eoc": 0.9893462340475302,
      "flux_l2_eoc": 1.0059094149555767,
      "macroconstant_pressure_l2_eoc": 0.9893462340475305,
      "macroconstant_projection_l2_eoc": 1.922725338301369,
      "rt0_integrated_quadratic_pressure_l2_relative_difference": 0.0001585614476282693,
      "rt0_integrated_quadratic_pressure_l2_eoc": 1.9880962259819517
    },
    {
      "n": 32,
      "macro_triangles": 2048,
      "grid_spacing": 0.03125,
      "macro_diameter": 0.04419417382415922,
      "pressure_l2": 0.032707265467522624,
      "flux_l2": 0.251934818810471,
      "macroconstant_pressure_l2": 0.03270726546752257,
      "macroconstant_projection_l2": 0.0011920123645848216,
      "computed_mean": -1.4440217684791312e-17,
      "macro_balance_max": 1.4992347641129555e-15,
      "algebraic_residual": 5.814045491800385e-16,
      "rt0_integrated_quadratic_pressure_l2": 0.002002155144536029,
      "flux_l2_relative_difference": -0.00027083872136246523,
      "macroconstant_pressure_l2_relative_difference": -0.0005154157328736142,
      "macroconstant_projection_l2_relative_difference": 0.0011013382745304057,
      "pressure_l2_eoc": 0.9975912392334961,
      "flux_l2_eoc": 1.0017562229004648,
      "macroconstant_pressure_l2_eoc": 0.9975912392334988,
      "macroconstant_projection_l2_eoc": 1.980733596702275,
      "rt0_integrated_quadratic_pressure_l2_relative_difference": 0.001136138732130254,
      "rt0_integrated_quadratic_pressure_l2_eoc": 1.9970632976181606
    },
    {
      "n": 64,
      "macro_triangles": 8192,
      "grid_spacing": 0.015625,
      "macro_diameter": 0.02209708691207961,
      "pressure_l2": 0.016360267137301345,
      "flux_l2": 0.12592748424959882,
      "macroconstant_pressure_l2": 0.016360267137301363,
      "macroconstant_projection_l2": 0.0002989988359405687,
      "computed_mean": 9.622294280808852e-19,
      "macro_balance_max": 2.9655097821823517e-15,
      "algebraic_residual": 3.342375699071531e-15,
      "rt0_integrated_quadratic_pressure_l2": 0.0005007926762727163,
      "flux_l2_relative_difference": -0.0005490363780449314,
      "macroconstant_pressure_l2_relative_difference": -0.00011366876070806331,
      "macroconstant_projection_l2_relative_difference": -0.0008426506826419988,
      "pressure_l2_eoc": 0.9994148407095819,
      "flux_l2_eoc": 1.0004573322125776,
      "macroconstant_pressure_l2_eoc": 0.9994148407095779,
      "macroconstant_projection_l2_eoc": 1.9951874279000767,
      "rt0_integrated_quadratic_pressure_l2_relative_difference": 0.000636748907468343,
      "rt0_integrated_quadratic_pressure_l2_eoc": 1.999268401991454
    }
  ],
  "figure5_comparison_fields": {
    "pressure_l2": "rt0_integrated_quadratic_pressure_l2",
    "flux_l2": "flux_l2",
    "macroconstant_pressure_l2": "macroconstant_pressure_l2",
    "macroconstant_projection_l2": "macroconstant_projection_l2"
  },
  "all_points_within_digitization_tolerance": {
    "pressure_l2": true,
    "flux_l2": true,
    "macroconstant_pressure_l2": true,
    "macroconstant_projection_l2": true
  }
}