Johnen, A., Remacle, J.-F., Geuzaine, C.: Geometrical validity of curvilinear finite elements. Journal of Computational Physics 233, 359–372 (2013)
Toulorge, T., Geuzaine, C., Remacle, J.-F., Lambrechts, J.: Robust untangling of curvilinear meshes. Journal of Computational Physics 254, 8–26 (2013)
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 79(11), 1309–1331 (2009)
Kroll, N., Bieler, H., Deconinck, H., Couaillier, V., van der Ven, H., Sørensen, K. (eds.): ADIGMA. NNFM, vol. 113. Springer, Heidelberg (2010)
Bassi, F., Rebay, S.: High-order accurate discontinuous finite element solution of the 2D Euler equations. Journal of Computational Physics 138(2), 251–285 (1997)
Dey, S., O’Bara, R.M., Shephard, M.S.: Curvilinear mesh generation in 3D. In: Proceedings of the 8th International Meshing Roundtable, pp. 407–417. John Wiley & Sons (1999)
Gargallo-Peiró, A., Roca, X., Peraire, J., Sarrate, J.: High-order mesh generation on CAD geometries. In: Proceedings of the VI International Conference on Adaptive Modeling and Simulation (ADMOS 2013), CIMNE, Barcelona (2013)
Xie, Z.Q., Sevilla, R., Hassan, O., Morgan, K.: The generation of arbitrary order curved meshes for 3D finite element analysis. Computational Mechanics 51(3), 361–374 (2013)
Sherwin, S.J., Peiró, J.: Mesh generation in curvilinear domains using high-order elements. International Journal for Numerical Methods in Engineering 53(1), 207–223 (2002)
Abgrall, R., Dobrzynski, C., Froehly, A.: A method for computing curved 2D and 3D meshes via the linear elasticity analogy: preliminary results. Rapport de recherche RR-8061, INRIA (September 2012)
Lu, Q., Shephard, M., Tendulkar, S., Beall, M.: Parallel curved mesh adaptation for large scale high-order finite element simulations. In: Proceedings of the 21st International Meshing Roundtable, pp. 419–436. Springer, Heidelberg (2013)
Persson, P.-O., Peraire, J.: Curved mesh generation and mesh refinement using lagrangian solid mechanics. In: Proceedings of the 47th AIAA Aerospace Sciences Meeting and Exhibit, Orlando (FL), USA, January 5-9 (2009)
Roca, X., Gargallo-Peiró, A., Sarrate, J.: Defining quality measures for high-order planar triangles and curved mesh generation. In: Quadros, W.R. (ed.) Proceedings of the 20th International Meshing Roundtable, pp. 365–383. Springer, Heidelberg (2012)
Luo, X.J., Shephard, M.S., O’Bara, R.M., Nastasia, R., Beall, M.W.: Automatic p-version mesh generation for curved domains. Engineering with Computers 20(3), 273–285 (2004)
Sahni, O., Luo, X.J., Jansen, K.E., Shephard, M.S.: Curved boundary layer meshing for adaptive viscous flow simulations. Finite Elements in Analysis and Design 46(1-2), 132–139 (2010)
Remacle, J.-F., Shephard, M.S.: An algorithm oriented mesh database. International Journal for Numerical Methods in Engineering 58(2), 349–374 (2003)
Dey, S., Shephard, M.S., Flaherty, J.E.: Geometry representation issues associated with p-version finite element computations. Computer Methods in Applied Mechanics and Engineering 150(1), 39–55 (1997)
Sevilla, R., Fernández-Méndez, S., Huerta, A.: NURBS-enhanced finite element method (NEFEM). International Journal for Numerical Methods in Engineering 76(1), 56–83 (2008)
Taylor, R.L.: On completeness of shape functions for finite element analysis. International Journal for Numerical Methods in Engineering 4(1), 17–22 (1972)
Lane, J.M., Riesenfeld, R.F.: A theoretical development for the computer generation and display of piecewise polynomial surfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence 2(1), 35–46 (1980)
Cohen, E., Schumacker, L.L.: Rates of convergence of control polygons. Computer Aided Geometric Design 2, 229–235 (1985)
Freitag, L., Knupp, P., Munson, T., Shontz, S.: A comparison of optimization software for mesh shape-quality improvement problems. Technical report, Argonne National Lab., IL, US (2002)
Fiacco, A.V., McCormick, G.P.: Nonlinear programming: sequential unconstrained minimization techniques, vol.4. Society for Industrial Mathematics (1990)
Waechter, A., Laird, C., Margot, F., Kawajir, Y.: Introduction to IPOPT: A tutorial for downloading, installing, and using IPOPT (2009)
Liu, D.C., Nocedal, J.: On the limited memory BFGS method for large scale optimization. Mathematical Programming 45(1), 503–528 (1989)
Fletcher, R., Reeves, C.M.: Function minimization by conjugate gradients. The Computer Journal 7(2), 149–154 (1964)
