References

[BKL+16]

N. Barral, M. G. Knepley, M. Lange, M. D. Piggott, and G. J. Gorman. Anisotropic mesh adaptation in Firedrake with PETSc DMPlex. In 25th Intl Meshing Roundtable. 2016.

[BR01]

Roland Becker and Rolf Rannacher. An optimal control approach to a posteriori error estimation in finite element methods. Acta numerica, 10:1–102, 2001. doi:10.1017/S0962492901000010.

[CPB13]

Jaime Carpio, Juan Luis Prieto, and Rodolfo Bermejo. Anisotropic “goal-oriented” mesh adaptivity for elliptic problems. SIAM Journal on Scientific Computing, 35(2):A861–A885, 2013. doi:10.1137/120874606.

[CWK+22]

Mariana CA Clare, Joseph G Wallwork, Stephan C Kramer, Hilary Weller, Colin J Cotter, and Matthew D Piggott. Multi-scale hydro-morphodynamic modelling using mesh movement methods. GEM-International Journal on Geomathematics, 13(1):1–39, 2022. doi:10.1007/s13137-021-00191-1.

[Clement75]

Ph Clément. Approximation by finite element functions using local regularization. Revue française d'automatique, informatique, recherche opérationnelle. Analyse numérique, 9(R2):77–84, 1975.

[DKGG22]

D Rhodri Davies, Stephan C Kramer, Sia Ghelichkhan, and Angus Gibson. Towards automatic finite-element methods for geodynamics via firedrake. Geoscientific Model Development, 15(13):5127–5166, 2022.

[FDKL98]

Charbel Farhat, Christoph Degand, Bruno Koobus, and Michel Lesoinne. Torsional springs for two-dimensional dynamic unstructured fluid meshes. Computer methods in applied mechanics and engineering, 163(1-4):231–245, 1998.

[FPP+09]

Patrick E Farrell, Matthew D Piggott, Christopher C Pain, Gerard J Gorman, and Cian R Wilson. Conservative interpolation between unstructured meshes via supermesh construction. Computer methods in applied mechanics and engineering, 198(33-36):2632–2642, 2009.

[HVH03]

Willem H Hundsdorfer, Jan G Verwer, and WH Hundsdorfer. Numerical solution of time-dependent advection-diffusion-reaction equations. Volume 33. Springer, 2003.

[LeV96]

Randall J. LeVeque. High-Resolution Conservative Algorithms for Advection in Incompressible Flow. SIAM Journal on Numerical Analysis, 33(2):627–665, 1996. doi:10.1137/0733033.

[LA11]

A Loseille and F Alauzet. Continuous mesh framework part I: well-posed continuous interpolation error. SIAM Journal on Numerical Analysis, 49(1):38–60, 2011. doi:10.1137/090754078.

[LDA10]

Adrien Loseille, Alain Dervieux, and Frédéric Alauzet. Fully anisotropic goal-oriented mesh adaptation for 3D steady Euler equations. Journal of computational physics, 229(8):2866–2897, 2010. doi:10.1016/j.jcp.2009.12.021.

[MCB18]

A. T. T. McRae, C. J. Cotter, and J. Budd, C. Optimal-transport-based mesh adaptivity on the plane and sphere using finite elements. SIAM Journal on Scientific Computing, 40(2):1121–1148, 2018. doi:10.1137/16M1109515.

[PUDOG01]

CC Pain, AP Umpleby, CRE De Oliveira, and AJH Goddard. Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations. Computer Methods in Applied Mechanics and Engineering, 190(29-30):3771–3796, 2001. doi:10.1016/S0045-7825(00)00294-2.

[PBA+19]

Michael A Park, Aravind Balan, William K Anderson, Marshall C Galbraith, Philip Caplan, Hugh A Carson, Todd R Michal, Joshua A Krakos, Dmitry S Kamenetskiy, Adrien Loseille, and others. Verification of unstructured grid adaptation components. In AIAA Scitech 2019 Forum, 1723. 2019. doi:10.2514/6.2019-1723.

[PPP+06]

PW Power, Christopher C Pain, MD Piggott, Fangxin Fang, Gerard J Gorman, AP Umpleby, Anthony JH Goddard, and IM Navon. Adjoint a posteriori error measures for anisotropic mesh optimisation. Computers & Mathematics with Applications, 52(8-9):1213–1242, 2006. doi:10.1016/j.camwa.2006.11.003.

[RCJ14]

A Riadh, G Cedric, and MH Jean. TELEMAC modeling system: 2D hydrodynamics TELEMAC-2D software release 7.0 user manual. Paris: R&D, Electricite de France, pages 134, 2014.

[VVP+92]

William T Vetterling, William T Vetterling, William H Press, William H Press, Saul A Teukolsky, Brian P Flannery, and Brian P Flannery. Numerical recipes: example book C. Cambridge University Press, 1992.

[Wal21]

JG Wallwork. Mesh adaptation and adjoint methods for finite element coastal ocean modelling. PhD thesis, Imperial College London, 2021. doi:10.25560/92820.

[WBHP22]

JG Wallwork, N Barral, DA Ham, and MD Piggott. Goal-oriented error estimation and mesh adaptation for tracer transport modelling. Computer-Aided Design, 145:103187, 2022. doi:10.1016/j.cad.2021.103187.

[Wil10]

Cian Wilson. Modelling multiple-material flows on adaptive unstructured meshes. PhD thesis, Imperial College London, 2010.