Underworld-Technical-Notes · lmoresi · Aug 13, 2026 · Aug 13, 2026 · Aug 13, 2026 · Aug 13, 2026
diff --git a/...ulus-and-spherical-stokes-benchmarks/annulus-and-spherical-stokes-benchmarks.md b/...ulus-and-spherical-stokes-benchmarks/annulus-and-spherical-stokes-benchmarks.md
diff --git a/articles/annulus-and-spherical-stokes-benchmarks/figures/banner.jpg b/articles/annulus-and-spherical-stokes-benchmarks/figures/banner.jpg
diff --git a/articles/annulus-and-spherical-stokes-benchmarks/figures/benchmark-fields.jpg b/articles/annulus-and-spherical-stokes-benchmarks/figures/benchmark-fields.jpg
diff --git a/...annulus-and-spherical-stokes-benchmarks/figures/boundary_metric_convergence.jpg b/...annulus-and-spherical-stokes-benchmarks/figures/boundary_metric_convergence.jpg
diff --git a/...and-spherical-stokes-benchmarks/figures/figure_3_kramer_annulus_convergence.jpg b/...and-spherical-stokes-benchmarks/figures/figure_3_kramer_annulus_convergence.jpg
diff --git a/...d-spherical-stokes-benchmarks/figures/figure_4_kramer_spherical_convergence.jpg b/...d-spherical-stokes-benchmarks/figures/figure_4_kramer_spherical_convergence.jpg
diff --git a/...d-spherical-stokes-benchmarks/figures/figure_5_thieulot_annulus_convergence.jpg b/...d-spherical-stokes-benchmarks/figures/figure_5_thieulot_annulus_convergence.jpg
diff --git a/...nd-spherical-stokes-benchmarks/figures/figure_7_kramer_boundary_convergence.jpg b/...nd-spherical-stokes-benchmarks/figures/figure_7_kramer_boundary_convergence.jpg
diff --git a/...nd-spherical-stokes-benchmarks/figures/figure_boundary_pressure_convergence.jpg b/...nd-spherical-stokes-benchmarks/figures/figure_boundary_pressure_convergence.jpg
diff --git a/...herical-stokes-benchmarks/figures/figure_p2p1_boundary_pressure_convergence.jpg b/...herical-stokes-benchmarks/figures/figure_p2p1_boundary_pressure_convergence.jpg
diff --git a/...us-and-spherical-stokes-benchmarks/figures/figures_4_5_thieulot_convergence.jpg b/...us-and-spherical-stokes-benchmarks/figures/figures_4_5_thieulot_convergence.jpg
diff --git a/articles/annulus-and-spherical-stokes-benchmarks/metadata.yml b/articles/annulus-and-spherical-stokes-benchmarks/metadata.yml
@@ -0,0 +1,36 @@
+# Validated in CI against schemas/article-metadata.schema.json.
+# `pixi run validate` checks this and the cross-file invariants a schema cannot
+# express -- that the article file is named <slug>.md, that canonical_path
+# matches the slug, and that no legacy DOI is ever paired with a new registrant.
+id: UWTN 2026-012
+slug: annulus-and-spherical-stokes-benchmarks
+title: Benchmarking Stokes Flow in Annulus and Spherical-Shell Geometries
+article_type: technical-note
+status: review
+authors:
+  - name: Thyagarajulu Gollapalli
+    orcid: 0000-0001-9394-4104
+    affiliation: Monash University
+publication_date: null
+version: 1.0.0
+# The deposit writes archive_doi and repository_record_id when the note is
+# published; leave them out until then. `doi` and `doi_registrant` were here
+# once and are not fields the schema knows -- every note made from this
+# template failed `pixi run validate` on all three of them.
+license: CC-BY-4.0
+canonical_path: /annulus-and-spherical-stokes-benchmarks/
+legacy_paths: []
+# Facets, from vocabulary.yml. Both keys must be present even when empty: a
+# note with no subject is normal -- many are purely about method.
+subjects:
+  - mantle-convection
+  - planetary
+methods:
+  - benchmarks-validation
+  - solvers
+  - finite-elements
+ghost_tags:
+  - Underworld Code
+figures: 9
+banner_credit: "Photo by <a href=\"https://unsplash.com/@theblowup?utm_source=underworld-technical-notes&utm_medium=referral&utm_campaign=api-credit\">the blowup</a> / <a href=\"https://unsplash.com/?utm_source=underworld-technical-notes&utm_medium=referral&utm_campaign=api-credit\">Unsplash</a>"
+source: native
diff --git a/articles/annulus-and-spherical-stokes-benchmarks/references.bib b/articles/annulus-and-spherical-stokes-benchmarks/references.bib
@@ -0,0 +1,70 @@
+% Pinned rather than resolved from doi.org at build time. Letting MyST fetch
+% citations over the network makes the build depend on doi.org answering, which
+% failed on CI for UWTN 2026-011 and would have published a broken citation.
+
+@article{Moresi_2025,
+  title   = {Underworld3: Mathematically Self-Describing Modelling in Python for Desktop, HPC and Cloud},
+  volume  = {10},
+  ISSN    = {2475-9066},
+  url     = {http://dx.doi.org/10.21105/joss.07831},
+  DOI     = {10.21105/joss.07831},
+  number  = {112},
+  journal = {Journal of Open Source Software},
+  publisher = {The Open Journal},
+  author  = {Moresi, Louis and Mansour, John and Giordani, Julian and Knepley, Matt and Knight, Ben and Graciosa, Juan Carlos and Gollapalli, Thyagarajulu and Lu, Neng and Beucher, Romain},
+  year    = {2025},
+  month   = aug,
+  pages   = {7831}
+}
+
+% No DOI: a preprint submitted to Computers & Geosciences, cited in the original
+% post by its author-hosted PDF. The URL is the only persistent handle there is.
+@unpublished{ThieulotPuckett_2018,
+  title   = {Incompressible Stokes flow in an annulus: an analytical solution and numerical benchmark},
+  author  = {Thieulot, Cedric and Puckett, Elbridge Gerry},
+  year    = {2018},
+  note    = {Preprint submitted to Computers \& Geosciences},
+  url     = {https://www.math.ucdavis.edu/~egp/PUBLICATIONS/JOURNAL_ARTICLES/SUBMITTED/CAPT-EGP-2018.pdf}
+}
+
+@article{Kramer_2021,
+  title   = {Analytical solutions for mantle flow in cylindrical and spherical shells},
+  volume  = {14},
+  ISSN    = {1991-9603},
+  url     = {http://dx.doi.org/10.5194/gmd-14-1899-2021},
+  DOI     = {10.5194/gmd-14-1899-2021},
+  number  = {4},
+  journal = {Geoscientific Model Development},
+  publisher = {Copernicus GmbH},
+  author  = {Kramer, Stephan C. and Davies, D. Rhodri and Wilson, Cian R.},
+  year    = {2021},
+  month   = apr,
+  pages   = {1899--1919}
+}
+
+@article{Thieulot_2017,
+  title   = {Analytical solution for viscous incompressible Stokes flow in a spherical shell},
+  volume  = {8},
+  ISSN    = {1869-9529},
+  url     = {http://dx.doi.org/10.5194/se-8-1181-2017},
+  DOI     = {10.5194/se-8-1181-2017},
+  number  = {6},
+  journal = {Solid Earth},
+  publisher = {Copernicus GmbH},
+  author  = {Thieulot, Cedric},
+  year    = {2017},
+  month   = nov,
+  pages   = {1181--1191}
+}
+
+@book{Boffi_2013,
+  title   = {Mixed Finite Element Methods and Applications},
+  ISBN    = {9783642365195},
+  ISSN    = {0179-3632},
+  url     = {http://dx.doi.org/10.1007/978-3-642-36519-5},
+  DOI     = {10.1007/978-3-642-36519-5},
+  series  = {Springer Series in Computational Mathematics},
+  publisher = {Springer Berlin Heidelberg},
+  author  = {Boffi, Daniele and Brezzi, Franco and Fortin, Michel},
+  year    = {2013}
+}
diff --git a/classification.yml b/classification.yml
@@ -312,3 +312,8 @@ moving-the-mesh-without-remaking-it:
   article_type: technical-note
   subjects: [mantle-convection, earthquakes-faults]
   methods: [meshing, solvers, parallel-hpc]
+
+annulus-and-spherical-stokes-benchmarks:
+  article_type: technical-note
+  subjects: [mantle-convection, planetary]
+  methods: [benchmarks-validation, solvers, finite-elements]