Johnen A., Remacle J.-F., Geuzaine C. Geometrical validity of curvilinear finite elements. Proceedings of the 20th International Meshing Roundtable 2012, 255-271. Springer, Berlin, Heidelberg. 10.1007/978-3-642-24734-7_14. W.R. Quadros (Ed.).
Johnen A., Remacle J.-F., Geuzaine C. Geometrical validity of curvilinear finite elements. Journal of Computational Physics 2013, 233:359-372. 10.1016/j.jcp.2012.08.051.
Discontinuous Galerkin Methods. Lecture Notes in Computational Science and Engineering 2000, vol. 11. Springer, Berlin. B. Cockburn, G. Karniadakis, C.-W. Shu (Eds.).
Kroll N., Bieler H., Deconinck H., Couaillier V., Van Der Ven H., Sorensen K. ADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications: Results of a Collaborative Research Project Funded by the European Union, 2006-2009. Notes on Numerical Fluid Mechanics and Multidisciplinary Design 2010, Springer.
Bassi F., Rebay S. High-order accurate discontinuous finite element solution of the 2D Euler equations. Journal of Computational Physics 1997, 138(2):251-285. 10.1006/jcph.1997.5454.
Bernard P.-E., Remacle J.-F., Legat V. Boundary discretization for high-order discontinuous Galerkin computations of tidal flows around shallow water islands. International Journal for Numerical Methods in Fluids 2009, 59(5):535-557. 10.1002/fld.1831.
Toulorge T., Desmet W. Curved boundary treatments for the discontinuous Galerkin method applied to aeroacoustic propagation. AIAA Journal 2010, 48(2):479-489. 10.2514/1.45353.
Remacle J.-F., Shephard M.S. An algorithm oriented mesh database. International Journal for Numerical Methods in Engineering 2003, 58(2):349-374. 10.1002/nme.774.
Geuzaine C., Remacle J.-F. Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering 2009, 79(11):1309-1331.
George P.L., Borouchaki H. Construction de maillages de degré 2. Partie 3: Tétraèdre P2 2011, Tech. rep., INRIA, France.
Knupp P.M. Winslow smoothing on two-dimensional unstructured meshes. Engineering with Computers 1999, 15:263-268. 10.1007/s003660050021.
Xie Z.Q., Sevilla R., Hassan O., Morgan K. The generation of arbitrary order curved meshes for 3D finite element analysis. Computational Mechanics 2013, 51(3):361-374. 10.1007/s00466-012-0736-4.
Persson P.-O., Peraire J. Curved mesh generation and mesh refinement using lagrangian solid mechanics. Proceedings of the 47th AIAA Aerospace Sciences Meeting and Exhibit 2009.
Li X., Shephard M., Beall M. Accounting for curved domains in mesh adaptation. International Journal for Numerical Methods in Engineering 2003, 58(2):247-276.
Luo X., Shephard M., O'Bara R., Nastasia R., Beall M. Automatic p-version mesh generation for curved domains. Engineering with Computers 2004, 20(3):273-285.
Shephard M., Flaherty J., Jansen K., Li X., Luo X., Chevaugeon N., Remacle J., Beall M., O'Bara R. Adaptive mesh generation for curved domains. Applied Numerical Mathematics 2005, 52(2):251-271.
Freitag L.A., Plassmann P. Local optimization-based simplicial mesh untangling and improvement. International Journal for Numerical Methods in Engineering 2000, 49(1):109-125.
López E.J., Nigro N.M., Storti M.A., Toth J.A. A minimal element distortion strategy for computational mesh dynamics. International Journal for Numerical Methods in Engineering 2007, 69:1898-1929.
López E.J., Nigro N.M., Storti M.A. Simultaneous untangling and smoothing of moving grids. International Journal for Numerical Methods in Engineering 2008, 76(7):994-1019.
Diachin L., Knupp P., Munson T., Shontz S. A comparison of two optimization methods for mesh quality improvement. Engineering with Computers 2006, 22(2):61-74.
Freitag L., Knupp P., Munson T., Shontz S. A comparison of optimization software for mesh shape-quality improvement problems 2002, Tech. rep., Argonne National Lab., IL, USA.
Fiacco A., McCormick G. Nonlinear Programming: Sequential Unconstrained Minimization Techniques, vol. 4 1990, Society for Industrial Mathematics.
A. Waechter, C. Laird, F. Margot, Y. Kawajir, Introduction to IPOPT: A tutorial for downloading, installing, and using IPOPT, 2009.
Liu D., Nocedal J. On the limited memory BFGS method for large scale optimization. Mathematical Programming 1989, 45(1):503-528.
Fletcher R., Reeves C. Function minimization by conjugate gradients. Computer Journal 1964, 7(2):149-154.
Hesthaven J., Warburton T. Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Texts in Applied Mathematics 2008, vol. 54. Springer-Verlag New York Inc.
Vos P., Sherwin S., Kirby R. From h to p efficiently: Implementing finite and spectral hp element methods to achieve optimal performance for low- and high-order discretisations. Journal of Computational Physics 2010, 229(13):5161-5181.
Bernard P., Remacle J., Comblen R., Legat V., Hillewaert K. High-order discontinuous Galerkin schemes on general 2D manifolds applied to the shallow water equations. Journal of Computational Physics 2009, 228(17):6514-6535.
Remacle J.-F., Geuzaine C., Compère G., Marchandise E. High-quality surface remeshing using harmonic maps. International Journal for Numerical Methods in Engineering 2010, 83(4):403-425.
Toulorge T., Desmet W. Spectral properties of discontinuous Galerkin space operators on curved meshes. Lecture Notes in Computational Science and Engineering 2011, vol. 76:495-502. Springer, Berlin, Heidelberg. 10.1007/978-3-642-15337-2_48. J.S. Hesthaven, E.M. Rønquist, T.J. Barth, M. Griebel, D.E. Keyes, R.M. Nieminen, D. Roose, T. Schlick (Eds.).
Seny B., Lambrechts J., Comblen R., Legat V., Remacle J.-F. Multirate time stepping for accelerating explicit discontinuous Galerkin computations with application to geophysical flows. International Journal for Numerical Methods in Fluids 2013, 71(1):41-64. 10.1002/fld.3646.
Lambrechts J., Hanert E., Deleersnijder E., Bernard P.-E., Legat V., Remacle J.-F., Wolanski E. A multiscale model of the whole Great Barrier Reef hydrodynamics. Estuarine, Coastal and Shelf Science 2008, 79:143-151. 10.1016/j.ecss.2008.03.016.
Botti L. Influence of reference-to-physical frame mappings on approximation properties of discontinuous piecewise polynomial spaces. Journal of Scientific Computing 2012, 52(3):675-703. 10.1007/s10915-011-9566-3.
