{
  "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": "P1 on one triangle per macrocell, constrained to zero mean",
  "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,
  "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": 0.11142926452022646,
      "flux_l2": 2.419076650196461,
      "macroconstant_pressure_l2": 0.24398051435425436,
      "macroconstant_projection_l2": 0.02324128473364148,
      "computed_mean": 7.806255641895632e-18,
      "macro_balance_max": 6.661338147750939e-16,
      "algebraic_residual": 1.0733665532887205e-16,
      "pressure_l2_relative_difference": -0.08884035636654197,
      "flux_l2_relative_difference": 0.18665406283266495,
      "macroconstant_pressure_l2_relative_difference": -0.022457055165121198,
      "macroconstant_projection_l2_relative_difference": -0.5968027893174488
    },
    {
      "n": 8,
      "macro_triangles": 128,
      "grid_spacing": 0.125,
      "macro_diameter": 0.1767766952966369,
      "pressure_l2": 0.030200320707971393,
      "flux_l2": 1.2767146724641019,
      "macroconstant_pressure_l2": 0.12863868924102162,
      "macroconstant_projection_l2": 0.007550681440305124,
      "computed_mean": -7.589415207398531e-18,
      "macro_balance_max": 9.43689570931383e-16,
      "algebraic_residual": 2.0335407698008596e-16,
      "pressure_l2_relative_difference": -0.046217783372038634,
      "flux_l2_relative_difference": 0.26058794815279995,
      "macroconstant_pressure_l2_relative_difference": -0.007828682900508088,
      "macroconstant_projection_l2_relative_difference": -0.5767637805997324,
      "pressure_l2_eoc": 1.8834924002921747,
      "flux_l2_eoc": 0.9220203435991713,
      "macroconstant_pressure_l2_eoc": 0.9234413192914083,
      "macroconstant_projection_l2_eoc": 1.6220110633692724
    },
    {
      "n": 16,
      "macro_triangles": 512,
      "grid_spacing": 0.0625,
      "macro_diameter": 0.08838834764831845,
      "pressure_l2": 0.007721936144956555,
      "flux_l2": 0.6472200022057589,
      "macroconstant_pressure_l2": 0.0651687172567124,
      "macroconstant_projection_l2": 0.002073886653609613,
      "computed_mean": 1.951563910473908e-18,
      "macro_balance_max": 5.273559366969494e-16,
      "algebraic_residual": 2.768099717329838e-16,
      "pressure_l2_relative_difference": -0.03367908457836244,
      "flux_l2_relative_difference": 0.28216455836539844,
      "macroconstant_pressure_l2_relative_difference": -0.0026826748550771162,
      "macroconstant_projection_l2_relative_difference": -0.559523041111742,
      "pressure_l2_eoc": 1.9675293407678893,
      "flux_l2_eoc": 0.9801080395071013,
      "macroconstant_pressure_l2_eoc": 0.9810731082459366,
      "macroconstant_projection_l2_eoc": 1.8642698047600892
    },
    {
      "n": 32,
      "macro_triangles": 2048,
      "grid_spacing": 0.03125,
      "macro_diameter": 0.04419417382415922,
      "pressure_l2": 0.001941659360829915,
      "flux_l2": 0.3247329623108654,
      "macroconstant_pressure_l2": 0.03268985221721547,
      "macroconstant_projection_l2": 0.0005311469643294278,
      "computed_mean": -1.2902005852577503e-17,
      "macro_balance_max": 1.7486012637846216e-15,
      "algebraic_residual": 5.680006074332849e-16,
      "pressure_l2_relative_difference": -0.029113522726122,
      "flux_l2_relative_difference": 0.28860716269154274,
      "macroconstant_pressure_l2_relative_difference": -0.0010475383360674106,
      "macroconstant_projection_l2_relative_difference": -0.5539207875617576,
      "pressure_l2_eoc": 1.9916725035833807,
      "flux_l2_eoc": 0.9950023605487129,
      "macroconstant_pressure_l2_eoc": 0.9953367430097929,
      "macroconstant_projection_l2_eoc": 1.9651540429853471
    },
    {
      "n": 64,
      "macro_triangles": 8192,
      "grid_spacing": 0.015625,
      "macro_diameter": 0.02209708691207961,
      "pressure_l2": 0.0004861202287172677,
      "flux_l2": 0.1625073286684559,
      "macroconstant_pressure_l2": 0.016358080204662343,
      "macroconstant_projection_l2": 0.0001335944691856769,
      "computed_mean": -4.892462303340839e-18,
      "macro_balance_max": 1.545204936226341e-15,
      "algebraic_residual": 1.1172713916492615e-15,
      "pressure_l2_relative_difference": -0.028680353590261,
      "flux_l2_relative_difference": 0.2897748827522968,
      "macroconstant_pressure_l2_relative_difference": -0.0002473269726886995,
      "macroconstant_projection_l2_relative_difference": -0.5535705171054504,
      "pressure_l2_eoc": 1.9979050459085927,
      "flux_l2_eoc": 0.9987490526158355,
      "macroconstant_pressure_l2_eoc": 0.9988394125000617,
      "macroconstant_projection_l2_eoc": 1.9912508175834192
    }
  ],
  "quadrature_check": {
    "n": 4,
    "assembly_order": 12,
    "error_order": 14,
    "relative_norm_changes": {
      "pressure_l2": -3.3306690738754696e-16,
      "flux_l2": 0.0,
      "macroconstant_pressure_l2": -1.1102230246251565e-16,
      "macroconstant_projection_l2": -1.8762769116165146e-14
    }
  },
  "formulation": "primal",
  "figure5_comparison_fields": {
    "pressure_l2": "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": false,
    "flux_l2": false,
    "macroconstant_pressure_l2": false,
    "macroconstant_projection_l2": false
  }
}