References#

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.

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/.

BDF+21

Wolfgang Bangerth, Juliane Dannberg, Menno Fraters, Rene Gassmoeller, Anne Glerum, Timo Heister, and John Naliboff. ASPECT: Advanced Solver for Problems in Earth's ConvecTion, User Manual. July 2021. doi:10.6084/m9.figshare.4865333. URL: https://doi.org/10.6084/m9.figshare.4865333, doi:10.6084/m9.figshare.4865333.

BDG+17

Wolfgang Bangerth, Juliane Dannberg, Rene Gassmoeller, Timo Heister, and others. ASPECT v1.5.0 [software]. mar 2017. doi:10.5281/zenodo.344623. URL: https://doi.org/10.5281/zenodo.344623, doi:10.5281/zenodo.344623.

BDG+18a

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.

BDG+18b

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.

BBC+89

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.

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. doi:10.1137/100791634.

CH19

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

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

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

DH16

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.

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.

DHPRF04

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. 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.

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.

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.

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.

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.

H+11

M. A. Heroux and others. Trilinos web page. 2011. http://trilinos.sandia.gov.

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.

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.

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. URL: http://gji.oxfordjournals.org/content/195/3/1406.abstract, arXiv:http://gji.oxfordjournals.org/content/195/3/1406.full.pdf+html, doi:10.1093/gji/ggt306.

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.

KHB12

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.

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.

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.

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.

Zho96

S. Zhong. Analytic solution for Stokes' flow with lateral variations in viscosity. Geophys. J. Int., 124:18–28, 1996.

JeanLGaRPaBPopov11

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