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V. Allken, R.S. Huismans, H. Fossen, and C. Thieulot. 3D numerical modelling of graben interaction and linkage: a case study of the Canyonlands grabens, Utah. Basin Research, 25:1–14, 2013.

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[BRVanko+04]

J. Badro, J.-P. Rueff, G. Vankó, G. Monaco, G. Fiquet, and F. Guyot. Electronic transitions in perovskite: Possible nonconvecting layers in the lower mantle. Science, 305:383–386, 2004.

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[BHK12]

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[BDF+24]

Wolfgang Bangerth, Juliane Dannberg, Menno Fraters, Rene Gassmoeller, Anne Glerum, Timo Heister, Robert Myhill, and John Naliboff. ASPECT: Advanced Solver for Planetary Evolution, Convection, and Tectonics, User Manual. December 2024. URL: https://doi.org/10.6084/m9.figshare.4865333, doi:10.6084/m9.figshare.4865333.

[BDG+17]

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Wolfgang Bangerth, Juliane Dannberg, Rene Gassmoeller, Timo Heister, and others. ASPECT v2.0.0 [software]. May 2018. URL: https://doi.org/10.5281/zenodo.1244587, doi:10.5281/zenodo.1244587.

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Wolfgang Bangerth, Juliane Dannberg, Rene Gassmoeller, Timo Heister, and others. ASPECT v2.0.1 [software]. June 2018. URL: https://doi.org/10.5281/zenodo.1297145, doi:10.5281/zenodo.1297145.

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[BSA+16]

S.J.H. Buiter, G. Schreurs, M. Albertz, T.V. Gerya, B. Kaus, W. Landry, L. le Pourhiet, Y. Mishin, D.L. Egholm, M. Cooke, B. Maillot, C. Thieulot, T. Crook, D. May, P. Souloumiac, and C. Beaumont. Benchmarking numerical models of brittle thrust wedges. Journal of Structural Geology, 92():140–177, 2016. doi:10.1016/j.jsg.2016.03.003.

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H.-P. Bunge, M.A. Richards, and J.R. Baumgardner. A sensitivity study of three-dimensional spherical mantle convection at $10^8$ Rayleigh number: Effects of depth-dependent viscosity, heating mode, and endothermic phase change. J. Geophys. Res., 102(B6):11,991–12,007, 1997. doi:10.1029/96JB03806.

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[BKS12]

Steffi Burchardt, Hemin Koyi, and Harro Schmeling. The influence of viscosity contrast on the strain pattern and magnitude within and around dense blocks sinking through newtonian rock salt. Journal of Structural Geology, 35:102–116, 2012. doi:10.1016/j.jsg.2011.07.007.

[BKSF12]

Steffi Burchardt, Hemin Koyi, Harro Schmeling, and Lukas Fuchs. Sinking of anhydrite blocks within a newtonian salt diapir: modelling the influence of block aspect ratio and salt stratification. Geophy. J. Int., 188(3):763–778, 2012. doi:10.1111/j.1365-246X.2011.05290.x.

[BSA+13]

C. Burstedde, G. Stadler, L. Alisic, L. C. Wilcox, E. Tan, M. Gurnis, and O. Ghattas. Large-scale adaptive mantle convection simulation. Geophysical Journal International, 192.3:889–906, 2013.

[BWG11]

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[BCC+94]

F. Busse, U. Christensen, R. Clever, L. Cserepes, C. Gable, E. Giannandrea, L. Guillou, G. Houseman, H.-C. Nataf, M. Ogawa, M. Parmentier, C. Sotin, and B. Travis. 3D convection at infinite Prandtl numbers in cartesian geometry — a benchmark comparison. Geophys. Astrophys. Fluid Dynamics, 75:39–59, 1994. doi:10.1080/03091929408203646.

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Thomas C. Clevenger and Timo Heister. Deal.II tutorial program step-63, http://www.dealii.org/developer/doxygen/deal.II/step_63.html. 2019.

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Thomas C. Clevenger and Timo Heister. Comparison between algebraic and matrix-free geometric multigrid for a Stokes problem on an adaptive mesh with variable viscosity. Numerical Linear Algebra with Applications, March 2021. URL: https://arxiv.org/abs/1907.06696, doi:10.1002/nla.2375.

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Thomas C. Clevenger, Timo Heister, Guido Kanschat, and Martin Kronbichler. A flexible, parallel, adaptive geometric multigrid method for fem. ACM Trans. Math. Softw., December 2020. URL: https://arxiv.org/abs/1904.03317, doi:10.1145/3425193.

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James AD Connolly. Computation of phase equilibria by linear programming: a tool for geodynamic modeling and its application to subduction zone decarbonation. Earth and Planetary Science Letters, 236(1-2):524–541, 2005.

[CSG+12]

F. Crameri, H. Schmeling, G. J. Golabek, T. Duretz, R. Orendt, S. J. H. Buiter, D. A. May, B. J. P. Kaus, T. V. Gerya, and P. J. Tackley. A comparison of numerical surface topography calculations in geodynamic modelling: an evaluation of the `sticky air' method. Geophysical Journal International, 189(1):38–54, 2012.

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FA Dahlen and Jeroen Tromp. Theoretical global seismology. Princeton University Press, 1998.

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J. Dannberg and T. Heister. Compressible magma/mantle dynamics: 3D, adaptive simulations in ASPECT. Geophysical Journal International, 207(3):1343–1366, 2016. URL: https://dx.doi.org/10.1093/gji/ggw329, doi:10.1093/gji/ggw329.

[DEF+17]

Juliane Dannberg, Zach Eilon, Ulrich Faul, Rene Gassmöller, Pritwiraj Moulik, and Robert Myhill. The importance of grain size to mantle dynamics and seismological observations. Geochemistry, Geophysics, Geosystems, 18(8):3034–3061, 2017. URL: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2017GC006944, arXiv:https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2017GC006944, doi:10.1002/2017GC006944.

[DGL+22]

Juliane Dannberg, Rene Gassmöller, Ranpeng Li, Carolina Lithgow-Bertelloni, and Lars Stixrude. An entropy method for geodynamic modelling of phase transitions: capturing sharp and broad transitions in a multiphase assemblage. Geophysical Journal International, 231(3):1833–1849, 07 2022. URL: https://doi.org/10.1093/gji/ggac293, arXiv:https://academic.oup.com/gji/article-pdf/231/3/1833/46842522/ggac293.pdf, doi:10.1093/gji/ggac293.

[DS15]

Juliane Dannberg and Stephan V. Sobolev. Low-buoyancy thermochemical plumes resolve controversy of classical mantle plume concept. Nature Communications, 6(11):6960, 2015. doi:10.1038/ncomms7960.

[DAlboussiereC13]

R. Deguen, T. Alboussière, and P. Cardin. Thermal convection in Earth's inner core with phase change at its boundary. Geophysical Journal International, 194(3):1310–1334, 2013. doi:10.1093/gji/ggt202.

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Anja Katrin Denner. Experiments on temporal variable step bdf2 algorithms. Master's thesis, University of Wisconsin Milwaukee, 2014. Master's Thesis.

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Y. Deubelbeiss and B. J. P. Kaus. Comparison of Eulerian and Lagrangian numerical techniques for the Stokes equations in the presence of strongly varying viscosity. Physics of the Earth and Planetary Interiors, 171:92–111, 2008.

[DB04]

Clark R. Dohrmann and Pavel B. Bochev. A stabilized finite element method for the stokes problem based on polynomial pressure projections. International Journal for Numerical Methods in Fluids, 46(2):183–201, August 2004. URL: https://doi.org/10.1002/fld.752, doi:10.1002/fld.752.

[DH03]

J. Donea and A. Huerta. Finite Element Methods for Flow Problems. John Wiley & Sons, Ltd, 2003.

[DHPRodriguezF04]

Jean Donea, Antonio Huerta, J.-Ph. Ponthot, and A. Rodríguez-Ferran. Arbitrary Lagrangian-Eulerian Methods, chapter 14, pages. American Cancer Society, 2004. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/0470091355.ecm009, arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/0470091355.ecm009, doi:10.1002/0470091355.ecm009.

[DMGT11]

T. Duretz, D. A. May, T. V. Gerya, and P. J. Tackley. Discretization errors and free surface stabilization in the finite difference and marker-in-cell method for applied geodynamics: A numerical study. Geoch. Geoph. Geosystems, 12:Q07004/1–26, 2011.

[FTvdBS19]

M. Fraters, C. Thieulot, A. van den Berg, and W. Spakman. The geodynamic world builder: a solution for complex initial conditions in numerical modeling. Solid Earth, 10(5):1785–1807, 2019. URL: https://www.solid-earth.net/10/1785/2019/, doi:10.5194/se-10-1785-2019.

[FBT+19]

M. R. T. Fraters, W. Bangerth, C. Thieulot, A. C. Glerum, and W. Spakman. Efficient and practical Newton solvers for nonlinear Stokes systems in geodynamics problems. Geophysics Journal International, 218(2):873–894, 04 2019. URL: https://doi.org/10.1093/gji/ggz183, arXiv:http://oup.prod.sis.lan/gji/article-pdf/218/2/873/28693654/ggz183.pdf, doi:10.1093/gji/ggz183.

[FB21]

M. R. T. Fraters and M. I. Billen. On the implementation and usability of crystal preferred orientation evolution in geodynamic modeling. Geochemistry, Geophysics, Geosystems, 22(10):e2021GC009846, 2021. e2021GC009846 2021GC009846. URL: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2021GC009846, arXiv:https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2021GC009846, doi:10.1029/2021GC009846.

[GDL+13]

Allison Gale, Colleen A Dalton, Charles H Langmuir, Yongjun Su, and Jean-Guy Schilling. The mean composition of ocean ridge basalts. Geochemistry, Geophysics, Geosystems, 14(3):489–518, 2013.

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E. Garzanti, G. Radeff, and M.G. Malusà. Slab breakoff: a critical appraisal of a geological theory as applied in space and time. Earth-Science Reviews, 177:303–319, 2018. doi:10.1016/j.earscirev.2017.11.012.

[GassmollerDB+24]

R. Gassmöller, J. Dannberg, W. Bangerth, E. G. Puckett, and C. Thieulot. Benchmarking the accuracy of higher-order particle methods in geodynamic models of transient flow. Geoscientific Model Development, 17(10):4115–4134, 2024. URL: https://gmd.copernicus.org/articles/17/4115/2024/, doi:10.5194/gmd-17-4115-2024.

[GassmollerDB+20]

Rene Gassmöller, Juliane Dannberg, Wolfgang Bangerth, Timo Heister, and Robert Myhill. On formulations of compressible mantle convection. Geophysical Journal International, 221(2):1264–1280, 2020. URL: https://doi.org/10.1093/gji/ggaa078, doi:10.1093/gji/ggaa078.

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Rene Gassmöller, Harsha Lokavarapu, Wolfgang Bangerth, and Elbridge Gerry Puckett. Evaluating the accuracy of hybrid finite element/particle-in-cell methods for modelling incompressible stokes flow. Geophysical Journal International, 219(3):1915–1938, 2019. doi:10.1093/gji/ggz405.

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Rene Gassmöller, Harsha Lokavarapu, Eric Heien, Elbridge Gerry Puckett, and Wolfgang Bangerth. Flexible and scalable particle-in-cell methods with adaptive mesh refinement for geodynamic computations. Geochemistry, Geophysics, Geosystems, 19(9):3596–3604, 2018. URL: https://doi.org/10.1029/2018GC007508, doi:10.1029/2018GC007508.

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A. Glerum, C. Thieulot, M. Fraters, C. Blom, and W. Spakman. Nonlinear viscoplasticity in ASPECT: benchmarking and applications to subduction. Solid Earth, 9(2):267–294, 2018. doi:10.5194/se-9-267-2018.

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William R Halter, Emilie Macherel, and Stefan M Schmalholz. A simple computer program for calculating stress and strain rate in 2d viscous inclusion-matrix systems. Journal of Structural Geology, 160:104617, 2022. doi:10.1016/j.jsg.2022.104617.

[HCB+16]

Lars N. Hansen, Clinton P. Conrad, Yuval Boneh, Philip Skemer, Jessica M. Warren, and David L. Kohlstedt. Viscous anisotropy of textured olivine aggregates: 2. Micromechanical model. Journal of Geophysical Research: Solid Earth, 121(10):7137–7160, 2016. doi:10.1002/2016JB013240.

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Robert N Harris and Marcia K McNutt. Heat flow on hot spot swells: evidence for fluid flow. Journal of Geophysical Research: Solid Earth, 2007.

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Gavin P Hayes, Ginevra L Moore, Daniel E Portner, Mike Hearne, Hanna Flamme, Maria Furtney, and Gregory M Smoczyk. Slab2, a comprehensive subduction zone geometry model. Science, 362(6410):58–61, 2018.

[HDGassmollerB17]

Timo Heister, Juliane Dannberg, Rene Gassmöller, and Wolfgang Bangerth. High accuracy mantle convection simulation through modern numerical methods. II: Realistic models and problems. Geophysical Journal International, 210(2):833–851, 2017. URL: https://doi.org/10.1093/gji/ggx195, doi:10.1093/gji/ggx195.

[HBH+05]

M. A. Heroux, R. A. Bartlett, V. E. Howle, R. J. Hoekstra, J. J. Hu, T. G. Kolda, R. B. Lehoucq, K. R. Long, R. P. Pawlowski, E. T. Phipps, A. G. Salinger, H. K. Thornquist, R. S. Tuminaro, J. M. Willenbring, A. Williams, and K. S. Stanley. An overview of the Trilinos project. ACM Trans. Math. Softw., 31:397–423, 2005.

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B. Hillebrand, C. Thieulot, T. Geenen, A. P. van den Berg, and W. Spakman. Using the level set method in geodynamical modeling of multi-material flows and Earth's free surface. Solid Earth, 5(2):1087–1098, 2014. URL: https://www.solid-earth.net/5/1087/2014/, doi:10.5194/se-5-1087-2014.

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G. Hirth and D Kohlstedt. Rheology of the upper mantle and the mantle wedge:a view from the experimentalists. In J. M. Eiler, editor, Inside the Subduction Factory, Geophys. Monogr. Ser. 138, pages 83–105. American Geophysical Union, Washington, DC, 2004.

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[KRB04]

Edouard Kaminski, Neil M Ribe, and Jules T Browaeys. D-rex, a program for calculation of seismic anisotropy due to crystal lattice preferred orientation in the convective upper mantle. Geophysical Journal International, 158(2):744–752, 2004.

[KR02]

Édouard Kaminski and Neil M. Ribe. Timescales for the evolution of seismic anisotropy in mantle flow. Geochemistry, Geophysics, Geosystems, 3(8):1–17, August 2002. URL: https://doi.org/10.1029/2001gc000222, doi:10.1029/2001gc000222.

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[KJKS08]

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[KSL03]

Richard F. Katz, Marc Spiegelman, and Charles H. Langmuir. A new parameterization of hydrous mantle melting. Geochemistry, Geophysics, Geosystems, 4(9):n/a–n/a, 2003. doi:10.1029/2002GC000433.

[KMuhlhausM10]

B. J. P. Kaus, H. Mühlhaus, and D. A. May. A stabilization algorithm for geodynamic numerical simulations with a free surface. Physics of the Earth and Planetary Interiors, 181(1):12–20, 2010.

[Kau10]

B.J.P. Kaus. Factors that control the angle of shear bands in geodynamic numerical models of brittle deformation. Tectonophysics, 484:36–47, 2010.

[KCK+08]

Peter Keken, Claire Currie, Scott King, Mark Behn, Amandine Cagnioncle, Jiangheng He, Richard Katz, Shu-Chuan Lin, E. Marc Parmentier, Marc Spiegelman, and Kelin Wang. A community benchmark for subduction zone modeling. Physics of the Earth and Planetary Interiors, 171:187–197, 12 2008. doi:10.1016/j.pepi.2008.04.015.

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[KLVK+10]

Scott D King, Changyeol Lee, Peter E Van Keken, Wei Leng, Shijie Zhong, Eh Tan, Nicola Tosi, and Masanori C Kameyama. A community benchmark for 2-D Cartesian compressible convection in the Earth's mantle. Geophysical Journal International, 180(1):73–87, 2010.

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M. Kronbichler, T. Heister, and W. Bangerth. High accuracy mantle convection simulation through modern numerical methods. Geophysical Journal International, 191:12–29, 2012. URL: http://dx.doi.org/10.1111/j.1365-246X.2012.05609.x, doi:10.1111/j.1365-246X.2012.05609.x.

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Z. Martinec, V. Klemann, W. van der Wal, R. E. M. Riva, G. Spada, Y. Sun, D. Melini, S. B. Kachuck, V. Barletta, K. Simon, G. A, and T. S. James. A benchmark study of numerical implementations of the sea level equation in gia modelling. Geophy. J. Int., 215(1):389–414, 2018.

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C. Morency and M.-P. Doin. Numerical simulations of the mantle lithosphere delamination. Journal of Geophysical Research: Solid Earth (1978–2012), 2004.

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L. Moresi, S. Quenette, V. Lemiale, C. Meriaux, B. Appelbe, and H. B. Mühlhaus. Computational approaches to studying non-linear dynamics of the crust and mantle. Phys. Earth Planet. Interiors, 163:69–82, 2007.

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Elvira Mulyukova and David Bercovici. Collapse of passive margins by lithospheric damage and plunging grain size. Earth and Planetary Science Letters, 484:341–352, 2018.

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Robert Myhill, Sanne Cottaar, Timo Heister, Ian Rose, Cayman Unterborn, Juliane Dannberg, and Rene Gassmoeller. Burnman – a python toolkit for planetary geophysics, geochemistry and thermodynamics. Journal of Open Source Software, 8(87):5389, 2023. URL: https://doi.org/10.21105/joss.05389, doi:10.21105/joss.05389.

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Takashi Nakagawa, Paul J Tackley, Frederic Deschamps, and James AD Connolly. Incorporating self-consistently calculated mineral physics into thermochemical mantle convection simulations in a 3-d spherical shell and its influence on seismic anomalies in earth's mantle. Geochemistry, Geophysics, Geosystems, 2009.

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F. Nimmo, G.D. Price, J. Brodholt, and D. Gubbins. The influence of potassium on core and geodynamo evolution. Geophysical Journal International, 156:363–376, 2004.

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Anthony Osei Tutu, Stephan V Sobolev, Bernhard Steinberger, Anton A Popov, and Irina Rogozhina. Evaluating the influence of plate boundary friction and mantle viscosity on plate velocities. Geochemistry, Geophysics, Geosystems, 19(3):642–666, 2018.

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H. Schmeling, A. Y. Babeyko, A. Enns, C. Faccenna, F. Funiciello, T. Gerya, G. J. Golabek, S. Grigull, B. J. P. Kaus, G. Morra, S. M. Schmalholz, and J. van Hunen. A benchmark comparison of spontaneous subduction models—towards a free surface. Physics of the Earth and Planetary Interiors, 171:198–223, 2008.

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Cedric Thieulot. Fieldstone: a computational geodynamics (self-)teaching tool. 2023. URL: https://cedrict.github.io/.

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[TSN+15]

N. Tosi, C. Stein, L. Noack, C. Hüttig, P. Maierova, H. Samual, D. R. Davies, C. R. Wilson, S. C. Kramer, C. Thieulot, A. Glerum, M. Fraters, W. Spakman, A. Rozel, and P. J. Tackley. A community benchmark for viscoplastic thermal convection in a 2-d square box. Geochem. Geophys. Geosyst., 16:2175–2196, 2015.

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Y. van Dinther, T. V. Gerya, L. A. Dalguer, F. Corbi, F. Funiciello, and P. M. Mai. The seismic cycle at subduction thrusts: 2. dynamic implications of geodynamic simulations validated with laboratory models. JGR Solid Earth, 118(4):1502–1525, 2013.

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J. van Hunen, A.P. van den Berg, and N.J. Vlaar. On the role of subducting oceanic plateaus in the development of shallow flat subduction. Tectonophysics, 352(3-4):317–333, 2002. doi:10.1016/S0040-1951(02)00263-9.

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P. E. van Keken, S. D. King, H. Schmeling, U. R. Christensen, D. Neumeister, and M.-P. Doin. A comparison of methods for the modeling of thermochemical convection. J. Geoph. Res., 102:22477–22495, 1997.

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M.J.R. Wortel and W. Spakman. Subduction and slab detachment in the Mediterranean-Carpathian region. Science, 290():1910–1917, 2000.

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H. Yamauchi and Y. Takei. Polycrystal anelasticity at near-solidus temperatures. Journal of Geophysical Research: Solid Earth, 121(11):7790–7820, 2016.

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Shijie Zhong, Michael Gurnis, and Gregory Hulbert. Accurate determination of surface normal stress in viscous flow from a consistent boundary flux method. Physics of the Earth and Planetary Interiors, 78(1-2):1–8, June 1993. URL: https://doi.org/10.1016/0031-9201(93)90078-n, doi:10.1016/0031-9201(93)90078-n.

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H. Čížková and C.R. Bina. Geodynamics of trench advance: Insights from a Philippine-Sea-style geometry. Earth Planet. Sci. Lett., 430():408–415, 2015. doi:10.1016/j.epsl.2015.07.004.

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Jean-Luc Guermond and Richard Pasquetti and Bojan Popov. Entropy viscosity method for nonlinear conservation laws. Journal of Computational Physics, 230:4248–4267, 2011.

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E. van der Wiel, D.J.J. van Hinsbergen, C. Thieulot, and W. Spakman. Linking rates of slab sinking to long-term lower mantle flow and mixing. Earth Planet. Sci. Lett., 625:118471, 2024. doi:10.1016/j.epsl.2023.118471.

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J. van Hunen and M.B. Allen. Continental collision and slab break-off: A comparison of 3-D numerical models with observations. Earth Planet. Sci. Lett., 302:27–37, 2011.

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