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AHT12

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AHFT13

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.

BRVanko+04

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BHK07

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BHK12

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BDF+21

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BDG+17

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BDG+18a

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BDG+18b

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BA18

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BBC+89

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Bui12

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BSA+16

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BRB97

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BSA+13

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BWG11

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BCC+93

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Cha86

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CY85

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CH19

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CH21

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.

CHKK20

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Con05

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CSG+12

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DT98

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DH16

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DAlboussiereC13

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DK08

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DB04

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DH03

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DHPRodriguezF04

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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.

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.

GRMalusa18

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+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.

GassmollerLBP19

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.

GassmollerLH+18

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.

Ger10

T. Gerya. Introduction to Numerical Geodynamic Modelling. Cambridge University Press, 2010.

GTF+18

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.

HM07

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

HDGassmollerB17

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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.

H+11

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HTG+14

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.

Hir00

Marc M. Hirschmann. Mantle solidus: experimental constraints and the effects of peridotite composition. Geochemistry, Geophysics, Geosystems, 2000.

HK04

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.

HB11

R. Huismans and C. Beaumont. Depth-dependent extension, two-stage breakup and cratonic underplating at rifted margins. Nature, 2011.

JH17

M. Jackson and M. Hudec. Salt Tectonics: Principles and Practice. Cambridge: Cambridge University Press, 2017. doi:10.1017/9781139003988.

JK06

Volker John and Petr Knobloch. On discontinuity—capturing methods for convection—diffusion equations. In Numerical Mathematics and Advanced Applications, pages 336–344. Springer Berlin Heidelberg, 2006. doi:10.1007/978-3-540-34288-5_27.

KW93

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KSL03

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KMuhlhausM10

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Kau10

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KMK13

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KH92

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KLVK+10

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KHB12

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MJP05

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MD04

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MQL+07

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.

NTDC09

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.

NB15

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PMB+12

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Qui14

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RK04

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Neil M. Ribe. On the relation between seismic anisotropy and finite strain. Journal of Geophysical Research, 97(B6):8737, 1992. URL: http://doi.wiley.com/10.1029/92JB00551, doi:10.1029/92JB00551.

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RDvHW11

J. Ritsema, A. Deuss, H. J. van Heijst, and J. H. Woodhouse. S40rts: a degree-40 shear-velocity model for the mantle from new rayleigh wave dispersion, teleseismic traveltime and normal-mode splitting function measurements. Geophysical Journal International, 184:1223–1236, 2011.

RvH00

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RP19

Jonathan M. Robey and Elbridge Gerry Puckett. Implementation of a volume-of-fluid method in a finite element code with applications to thermochemical convection in a density stratified fluid in the Earth's mantle. Computers & Fluids, 190(2):217–253, 2019. Special Issue on Modeling Fluid Interfaces. doi:https://doi.org/10.1016/j.compfluid.2019.05.015.

RB04

E. H. Rutter and K. H. Brodie. Experimental grain size-sensitive flow of hot-pressed brazilian quartz aggregates. J. Struct. Geol., 26:2011–2023, 2004.

RGWD06

E. Rybacki, M. Gottschalk, R. Wirth, and G. Dresen. Influence of water fugacity and activation volume on the flow properties of fine-grained anorthite aggregates. J. Geophys. Res., 2006.

Sch11

S. M. Schmalholz. A simple analytical solution for slab detachment. Earth Planet. Sci. Lett., 304():45–54, 2011.

SBE+08

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.

Sch00

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SP03

D. W. Schmid and Y. Y. Podladchikov. Analytical solutions for deformable elliptical inclusions in general shear. Geophysical Journal International, 155(1):269–288, 2003.

STO01

G. Schubert, D. L. Turcotte, and P. Olson. Mantle Convection in the Earth and Planets, Part 1. Cambridge, 2001.

SS11

Gideon Simpson and Marc Spiegelman. Solitary wave benchmarks in magma dynamics. Journal of Scientific Computing, 49(3):268–290, 2011.

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SC06

B. Steinberger and A.R. Calderwood. Models of large-scale viscous flow in the Earth's mantle with constraints from mineral physics and surface observations. Geophy. J. Int., 167:1461–1481, 2006. doi:10.1111/j.1365-246X.2006.03131.x.

SLB11

Lars Stixrude and Carolina Lithgow-Bertelloni. Thermodynamics of mantle minerals-ii. phase equilibria. Geophysical Journal International, 184(3):1180–1213, 2011.

TMK14

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Thi11

C. Thieulot. FANTOM: two- and three-dimensional numerical modelling of creeping flows for the solution of geological problems. Phys. Earth. Planet. Inter., 188:47–68, 2011.

Thi15

C. Thieulot. ELEFANT: a user-friendly multipurpose geodynamics code. Technical Report, Utrecht University, 2015.

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Thi19

C. Thieulot. The finite element method in geodynamics. 2019. URL: https://github.com/cedrict/fieldstone/blob/master/manual.pdf.

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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vKKS+97

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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