Discontinuous Galerkin Methods for Isogeometric Analysis for Elliptic Equations on Surfaces

Farin, G.: Curves and Surfaces for CAGD, 5th edn. Morgan Kaufmann Publishers, San Francisco (2002)

Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput. Methods Appl. Mech. Eng. 194, 4135–4195 (2005)

Bazilevs, Y., de Veiga, B., Cottrell, J.A., Hughes, T.J.R., Sangalli, G.: Isogeometric analysis: approximation, stability and error estimates for h-refined meshes. Math. Models Methods Appl. Sci. 16(07), 1031–1090 (2006). L

Bazilevs, Y., Calo, V.M., Cottrell, J.A., Hughes, T.J.R., Reali, A., Scovazzi, G.: Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comp. Methods Appl. Mech. Eng. 197, 173–201 (2007)

Bazilevs, Y., Calo, V.M., Hughes, T.J.R., Zhang, Y.: Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput. Mech. 43, 3–37 (2008)

Cottrell, J.A., Reali, A., Bazilevs, Y., Hughes, T.J.R.: Isogeometric analysis of structural vibrations. Comput. Methods Appl. Mech. Eng. 195, 5257–5296 (2006)

Cottrell, J.A., Hughes, T.J.R., Reali, A.: Studies of refinement and continuity in isogeometric analysis. Comput. Methods Appl. Mech. Eng. 196, 4160–4183 (2007)

Cottrell, J.A., Hughes, T.J.R., Bazilevs, Y.: Isogeometric Analysis: Toward Integration of CAD and FEA. Wiley, Chichester (2009)

Reed, W.H., Hill, T.R.: Triangular mesh methods for the neutron transport equation, Los Alamos Report LA-UR-73-479 (1973)

Cockburn, B., Shu, C.-W.: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework. Math. Comput. 52(186), 411–435 (1989)

Cockburn, B., Lin, S.Y., Shu, C.-W.: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems. J. Comput. Phys. 84(1), 90–113 (1989)

Cockburn, B., Hou, S., Shu, C.-W.: The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case. Math. Comput. 54(190), 545–581 (1990)

Cockburn, B., Shu, C.-W.: The Runge-Kutta local projection $$P^{1}$$ P 1 -discontinuous-Galerkin finite element method for scalar conservation laws. RAIRO Model. Math. Anal. Numer. 25(3), 337–361 (1991)

Cockburn, B., Shu, C.-W.: The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. J. Comput. Phys. 141(2), 199–224 (1998)

Brezzi, F., Manzini, G., Marini, D., Pietra, P., Russo, A.:Discontinuous finite elements for diffusion problems, Atti Convegno in onore di F. Brioschi (Milano 1997), Istituto Lombardo. Accademia di Scienze e Lettere, pp. 197–217 (1999)

Brezzi, F., Manzini, G., Marini, D., Pietra, P., Russo, A.: Discontinuous Galerkin approximations for elliptic problems. Numer. Methods Partial Differ. Equ. 16, 365–378 (2000)

Castillo, P., Cockburn, B., Perugia, I., et al.: An a priori error analysis of the local discontinuous Galerkin method for elliptic problems. SIAM J. Numer. Anal. 38, 1676–1706 (2000)

Cockburn, B., Dawson, C.: Some extensions of the local discontinuous Galerkin method for convection-diffusion equations in multidimensions. In: Whiteman, J.R. (ed.) Proceedings of the Conference on the Mathematics of Finite Elements and Applications: MAFELAP X, pp. 225–238. Elsevier, NewYork (2000)

Cockburn, B., Kanschat, G., Perugia, I., et al.: Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids. SIAM J. Numer. Anal. 39(1), 264–285 (2001)

Arnold, D.N.: An interior penalty finite element method with discontinuous elements. Ph.D. thesis, The University of Chicago, Chicago, IL (1979)

Arnold, D.N.: An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19, 742–760 (1982)

Baker, G.A.: Finite element methods for elliptic equations using nonconforming elements. Math. Comput. 31, 45–59 (1977)

Douglas Jr, J., Dupont, T.: Interior Penalty Procedures for Elliptic and Parabolic Galerkin Methods, Computing methods in applied sciences. Springer, Berlin (1976)

Wheeler, M.F.: An elliptic collocation-finite element method with interior penalties. SIAM J. Numer. Anal. 15, 152–161 (1978)

Arnold, D.N., Brezzi, F., Cockburn, B., Marini, L.D.: Unified analysis of Discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39, 1749–1779 (2002)

Auricchio, F., da Veiga, L.B., Buffa, A., et al.: A fully locking-free isogeometric approach for plane linear elasticity problems: a stream function formulation. Comp. Methods Appl. Mech. Eng. 197(1), 160–172 (2007)

Bazilevs, Y., Hughes, T.J.R.: NURBS-based isogeometric analysis for the computation of flows about rotating components. Comput. Mech. 43(1), 143–150 (2008)

Brunero, F.: Discontinuous Galerkin Methods for isogeometric analysis. master’s thesis, Università degli Studi di Milano (2012)

Evans, J.A., Hughes, T.J.R.: Isogeometric divergence-conforming B-splines for the steady Navier-Stokes equations. Math. Models Methods Appl. Sci. 23(08), 1421–1478 (2013)

Nguyen, V.P., Kerfriden, P., Brino, M., et al.: Nitsche’s method for two and three dimensional NURBS patch coupling. Comput. Mech. 53, 1163–1182 (2014)

Imran Özcan, Ali: A Nitsche-based mortar method for non-matching multi-patch discretizations in the Finite Cell Method. Master’s thesis, Technische Universität München, Germany (2012)

Ruess, M., Schillinger, D., et al.: Weak coupling for isogeometric analysis of non-matching and trimmed multi-patch geometries. Comput. Methods Appl. Mech. Eng. 269, 46–71 (2014)

Dziuk, G., Elliot, C.M.: Finite element methods for surface PDEs. Acta Numerica 22, 289–396 (2013)

Langer, U., Moore, S.E.: Discontinuous Galerkin Isogeometric Analysis of Elliptic PDEs on Surfaces, preprint http://arxiv.org/pdf/1402.1185 , 2014. arXiv preprint arXiv:1402.1185 (2014)

Xu, G.L., Zhang, Q.: Geometric Partial Differential Equation Methods in Computational Geometry. Science Press, Beijing (2013)

Bonito, A., Cascón, J.M., Morin, P., Nochetto, R.H., Gianazza, U.: AFEM for geometric PDE: the Laplace–Beltrami operator. In: Brezzi, F., Franzone, P.C., Gilardi, G. (eds.) Analysis and Numerics of Partial Differential Equations, pp. 257–306. Springer, Milan (2013)

Gould, P.L.: Introduction to Linear Elasticity. Springer, Berlin (1999)