Pith Number

pith:2HQ6BPHB

pith:2026:2HQ6BPHBAG4KPW5CSAVYRQSBVK

not attested not anchored not stored refs pending

Discretization of the Burgers' equation as a port-Hamiltonian system

Ghislain Haine, Lorenzo Agostini, Michel Fourni\'e

A dedicated finite element method discretizes the Burgers equation into a finite-dimensional port-Hamiltonian system.

arxiv:2603.12992 v2 · 2026-03-13 · math.NA · cs.NA · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2HQ6BPHBAG4KPW5CSAVYRQSBVK}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Applying a dedicated finite element method, a finite-dimensional port-Hamiltonian system is derived. The relationship between time step, spatial resolution, and viscosity required to achieve numerical stability is analyzed. Numerical experiments validate the effectiveness of the approach.

C2weakest assumption

That the chosen finite-element spaces and time-stepping scheme preserve the port-Hamiltonian structure and that the derived stability relation between time step, mesh size, and viscosity is both necessary and sufficient for the nonlinear problem.

C3one line summary

Port-Hamiltonian discretizations of the Burgers' equation are derived via finite elements, yielding structure-preserving schemes whose stability conditions are analyzed and tested numerically.

Receipt and verification

First computed	2026-05-18T02:45:04.845282Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1e1e0bce101b8a7dba2902b88c241aa9b4781c8a9e2e47e0b21e275625358f1

Aliases

arxiv: 2603.12992 · arxiv_version: 2603.12992v2 · doi: 10.48550/arxiv.2603.12992 · pith_short_12: 2HQ6BPHBAG4K · pith_short_16: 2HQ6BPHBAG4KPW5C · pith_short_8: 2HQ6BPHB

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2HQ6BPHBAG4KPW5CSAVYRQSBVK \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: d1e1e0bce101b8a7dba2902b88c241aa9b4781c8a9e2e47e0b21e275625358f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7cb4b54010b1e12f5774f1ebbc049f9350173edd136a19a466dd9b468e994224",
    "cross_cats_sorted": [
      "cs.NA",
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-03-13T13:49:21Z",
    "title_canon_sha256": "fe76918f9e3a20ce03efdb762754dd493259a41c552c018213e5bde2540db6a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.12992",
    "kind": "arxiv",
    "version": 2
  }
}