{"id": "operators", "title": "Summation-by-parts operators", "description": "Gauss\u2013Lobatto collocation operators: the SBP identity M D + (M D)^T = B, quadrature exactness to degree 2p-1, exact differentiation of degree-p polynomials, skew-symmetry of the flux-differencing matrix M S and consistency of the p-multigrid transfers.", "passed": true, "checks": [{"name": "largest defect over all identities and degrees", "value": 6.217248937900877e-15, "expected": "< 1e-11", "passed": true}], "charts": [], "tables": [{"id": "defects", "title": "Maximum defects per polynomial degree", "columns": ["p", "SBP", "quadrature (deg <= 2p-1)", "differentiation", "skew(M S)", "Pi I - 1"], "rows": [[1, 0.0, 0.0, 0.0, 0.0, 2.220446049250313e-16], [2, 0.0, 2.220446049250313e-16, 0.0, 0.0, 4.996003610813204e-16], [3, 3.3306690738754696e-16, 5.551115123125783e-17, 8.881784197001252e-16, 4.440892098500626e-16, 0.0], [4, 1.1102230246251565e-15, 3.3306690738754696e-16, 1.7763568394002505e-15, 8.881784197001252e-16, 4.440892098500626e-16], [5, 1.38663231539537e-15, 2.220446049250313e-16, 2.6645352591003757e-15, 1.9984014443252818e-15, 4.440892098500626e-16], [6, 2.2128382914968496e-15, 1.942890293094024e-16, 4.440892098500626e-15, 1.5543122344752192e-15, 4.440892098500626e-15], [7, 1.893611337086567e-15, 1.1102230246251565e-16, 3.1086244689504383e-15, 2.220446049250313e-15, 1.887379141862766e-15], [8, 2.55351295663786e-15, 4.440892098500626e-16, 6.217248937900877e-15, 3.774758283725532e-15, 1.1423154089307275e-15]]}], "provenance": {"version": "0.4.0", "commit": "39979fcf902ad6116eb550b881b4278d4599c8e2", "dirty": false, "describe": "39979fcf90", "device": {"platform": "cpu", "device": "cpu:0", "device_kind": "cpu", "jax": "0.11.2", "x64": true}, "timestamp": "2026-11-12T10:22:15-0500"}, "wall_time": 0.29, "level": "quick"}