[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.
[AHT11] V. Allken, R. Huismans, and C. Thieulot. Three dimensional numerical modelling of upper crustal extensional systems. J. Geophys. Res., 116:B10409, 2011.
[AHT12] V. Allken, R. Huismans, and C. Thieulot. Factors controlling the mode of rift interaction in brittle-ductile coupled systems: a 3d numerical study. Geochem. Geophys. Geosyst., 13(5):Q05010, 2012.
[BBC89] B. Blankenbach, F. Busse, U. Christensen, L. Cserepes, D. Gunkel, U. Hansen, H. Harder, G. Jarvis, M. Koch, G. Marquart, D. Moore, P. Olson, H. Schmeling, and T. Schnaubelt. A benchmark comparison for mantle convection codes. Geophys. J. Int., 98:23–38, 1989.
[BHK07] W. Bangerth, R. Hartmann, and G. Kanschat. deal.II – a general purpose object oriented finite element library. ACM Trans. Math. Softw., 33(4):24, 2007.
[BHK12] W. Bangerth, T. Heister, and G. Kanschat. deal.II Differential Equations Analysis Library, Technical Reference, 2012. http://www.dealii.org/.
[BHPeGeS14] S. Brune, C. Heine, M Pẽrez Gussinyẽ, and S. V. Sobolev. Rift migration explains continental margin asymmetry and crustal hyperextension. Nat. Comm., 5(4014), 2014.
[BKEO03] Thorsten W. Becker, James B. Kellogg, Göran Ekström, and Richard J. O’Connell. Comparison of azimuthal seismic anisotropy from surface waves and finite strain from global mantle-circulation models. Geophysical Journal International, 155(2):696–714, nov 2003.
[BR86] V. Barcilon and F. M. Richter. Nonlinear waves in compacting media. Journal of Fluid mechanics, 164:429–448, 1986.
[BRV04] 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.
[BSA13] 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.
[Bui12] S. J. H. Buiter. A review of brittle compressional wedge models. Tectonophysics, 530:1–17, 2012.
[BWG11] C. Burstedde, L. C. Wilcox, and O. Ghattas. p4est: Scalable algorithms for parallel adaptive mesh refinement on forests of octrees. SIAM J. Sci. Comput., 33(3):1103–1133, 2011.
[Cha86] D. S. Chapman. Thermal gradients in the continental crust. Geol. Soc. London Spec. Publ., 24:63–70, 1986.
[CSG12] 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.
[DAC13] 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.
[DB14] C. R. Dohrmann and P. B. Bochev. A stabilized finite element method for the stokes problem based on polynomial pressure projections. International Journal for Numerical Methods in Fluids, 46:183–201, 20014.
[DH16] J. Dannberg and T. Heister. Compressible magma/mantle dynamics: 3D, adaptive simulations in ASPECT. Geophysical Journal International, 207(3):1343–1366, 2016.
[DHPRF04] J. Donea, A. Huerta, J.-Ph. Ponthot, and A. Rodríguez-Ferran. Arbitrary Lagrangian-Eulerian Methods. John Wiley & Sons, Ltd, 2004.
[DK08] 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.
[DMGT11] T. Duretz, D. A. May, T. V. Garya, 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.
[DT98] FA Dahlen and Jeroen Tromp. Theoretical global seismology. Princeton University Press, 1998.
[GHPB17] R. Gassmöller, E. Heien, E. G. Puckett, and W. Bangerth. Flexible and scalable particle-in-cell methods for massively parallel computations. submitted, 2017.
[GPP11] J.-L. Guermond, R. Pasquetti, and B. Popov. Entropy viscosity method for nonlinear conservation laws. J. Comput. Phys., 230:4248–4267, 2011.
[GTZ12] M. Gurnis, M. Turner, S. Zahirovic, L. DiCaprio, S. Spasojevic, R. D. Müller, J. Boyden, M. Seton, V. C. Manea, and D. J. Bower. Plate tectonic reconstructions with continuously closing plates. Computers & Geosciences, 38:35–42, 2012.
[H11] M. A. Heroux et al. Trilinos web page, 2011. http://trilinos.sandia.gov.
[HB11] R. Huismans and C. Beaumont. Depth-dependent extension, two-stage breakup and cratonic underplating at rifted margins. Nature, 473(71–75), 2011.
[HBH05] 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.
[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.
[Jea11] Jean-Luc Guermond and Richard Pasquetti and Bojan Popov. Entropy viscosity method for nonlinear conservation laws. Journal of Computational Physics, 230:4248–4267, 2011.
[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.
[KHB12] M. Kronbichler, T. Heister, and W. Bangerth. High accuracy mantle convection simulation through modern numerical methods. Geophysical Journal International, 191:12–29, 2012.
[KLVK10] 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.
[KMK13] Tobias Keller, Dave A. May, and Boris J. P. Kaus. Numerical modelling of magma dynamics coupled to tectonic deformation of lithosphere and crust. Geophysical Journal International, 195(3):1406–1442, 2013.
[KMM10] 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.
[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.
[LT07] B. Lund and J. Townend. Calculating horizontal stress orientations with full or partial knowledge of the tectonic stress tensor. Geophys. J. Int., 170:1328–1335, 2007.
[MD04] C. Morency and M.-P. Doin. Numerical simulations of the mantle lithosphere delamination. Journal of Geophysical Research: Solid Earth (1978–2012), 109(B3), 2004.
[MJ83] Dan McKenzie and James Jackson. The relationship between strain rates, crustal thickening, palaeomagnetism, finite strain and fault movements within a deforming zone. Earth and Planetary Science Letters, 65(1):182–202, 1983.
[MQL07] 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.
[NB15] J. Naliboff and S. Buiter. Rift reactivation and migration during multiphase extension. Earth Planet. Sci. Lett., 421(58–67), 2015.
[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.
[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.
[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., 111(B3), 2006.
[Rib92] Neil M. Ribe. On the relation between seismic anisotropy and finite strain. Journal of Geophysical Research, 97(B6):8737, 1992.
[RvH00] J. Ritsema and H. J. van Heijst. Seismic imaging of structural heterogeneity in earth’s mantle: Evidence for large-scale mantle flow. Sci. Progr., 83:243–259, 2000.
[SBE08] 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] Harro Schmeling. Partial melting and melt segregation in a convecting mantle. In Physics and Chemistry of Partially Molten Rocks, pages 141–178. Springer, 2000.
[Sch06] H Schmeling. A model of episodic melt extraction for plumes. Journal of Geophysical Research: Solid Earth, 111(B3), 2006.
[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.
[SS11] Gideon Simpson and Marc Spiegelman. Solitary wave benchmarks in magma dynamics. Journal of Scientific Computing, 49(3):268–290, 2011.
[STO01] G. Schubert, D. L. Turcotte, and P. Olson. Mantle Convection in the Earth and Planets, Part 1. Cambridge, 2001.
[Thi15] C. Thieulot. ELEFANT: a user-friendly multipurpose geodynamics code. Technical report, Utrecht University, 2015.
[TMK14] M. Thielmann, D. A. May, and B. J. P. Kaus. Discretization errors in the hybrid finite element particle-in-cell method. Pure and Applied Geophysics, 171:2165–2184, 2014.
[TS14] D. L. Turcotte and G. Schubert. Geodynamics. Cambridge, 3rd edition, 2014.
[vKKS97] 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.
[Wil99] S. D. Willett. Rheological dependence of extension in wedge models of convergent orogens. Tectonophysics, 305:419–435, 1999.
[Wor12] J. Worthen. Inverse Problems in Mantle Convection: Models, Algorithms, and Applications. PhD thesis, University of Texas at Austin, in preparation, 2012.
[ZGH93] 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, jun 1993.
[Zho96] S. Zhong. Analytic solution for Stokes’ flow with lateral variations in viscosity. Geophys. J. Int., 124:18–28, 1996.