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Book
Cangiani A, Dong Z, Georgoulis EH, Houston P. $hp$-version discontinuous Galerkin methods on polygonal and polyhedral meshes. Springer, Cham; 2017 p. viii+131.
Book Chapter
Cangiani A, Süli E. Enhanced residual-free bubble method for convection-diffusion problems. In: Internat. J. Numer. Methods Fluids. Vol. 47. Internat. J. Numer. Methods Fluids. ; 2005. pp. 1307–1313. Available from: https://doi.org/10.1002/fld.859
Cangiani A, Chapman J, Georgoulis EH, Jensen M. Implementation of the continuous-discontinuous Galerkin finite element method. In: Numerical mathematics and advanced applications 2011. Numerical mathematics and advanced applications 2011. Springer, Heidelberg; 2013. pp. 315–322.
Antonietti PF, Cangiani A, Collis J, Dong Z, Georgoulis EH, Giani S, Houston P. Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains. In: Building bridges: connections and challenges in modern approaches to numerical partial differential equations. Vol. 114. Building bridges: connections and challenges in modern approaches to numerical partial differential equations. Springer, [Cham]; 2016. pp. 279–308.
Cangiani A, Sutton OJ, Gyrya V, Manzini G. Virtual element methods for elliptic problems on polygonal meshes. In: Generalized barycentric coordinates in computer graphics and computational mechanics. Generalized barycentric coordinates in computer graphics and computational mechanics. CRC Press, Boca Raton, FL; 2018. pp. 263–279.
Journal Article
Cangiani A, Georgoulis EH, Sabawi YA. Adaptive discontinuous Galerkin methods for elliptic interface problems. Math. Comp. [Internet]. 2018 ;87:2675–2707. Available from: https://doi.org/10.1090/mcom/3322
Cangiani A, Georgoulis EH, Metcalfe S. Adaptive discontinuous Galerkin methods for nonstationary convection-diffusion problems. IMA J. Numer. Anal. [Internet]. 2014 ;34:1578–1597. Available from: https://doi.org/10.1093/imanum/drt052
Cangiani A, Georgoulis EH, Sutton OJ. Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods. Mathematical Models and Methods in Applied Sciences [Internet]. 2021 ;31:711-751. Available from: https://doi.org/10.1142/S0218202521500172
Cangiani A, Georgoulis EH, Kyza I, Metcalfe S. Adaptivity and blow-up detection for nonlinear evolution problems. SIAM J. Sci. Comput. [Internet]. 2016 ;38:A3833–A3856. Available from: https://doi.org/10.1137/16M106073X
L. da Veiga B, Brezzi F, Cangiani A, Manzini G, Marini LD, Russo A. Basic principles of virtual element methods. Math. Models Methods Appl. Sci. [Internet]. 2013 ;23:199–214. Available from: https://doi.org/10.1142/S0218202512500492
Cangiani A, Manzini G, Sutton OJ. Conforming and nonconforming virtual element methods for elliptic problems. IMA J. Numer. Anal. [Internet]. 2017 ;37:1317–1354. Available from: https://doi.org/10.1093/imanum/drw036
Cangiani A, Manzini G, Russo A. Convergence analysis of the mimetic finite difference method for elliptic problems. SIAM J. Numer. Anal. [Internet]. 2009 ;47:2612–2637. Available from: https://doi.org/10.1137/080717560
Cangiani A, Georgoulis EH, Sabawi YA. Convergence of an adaptive discontinuous Galerkin method for elliptic interface problems. J. Comput. Appl. Math. [Internet]. 2020 ;367:112397, 15. Available from: https://doi.org/10.1016/j.cam.2019.112397
Cangiani A, Gardini F, Manzini G. Convergence of the mimetic finite difference method for eigenvalue problems in mixed form. Comput. Methods Appl. Mech. Engrg. [Internet]. 2011 ;200:1150–1160. Available from: https://doi.org/10.1016/j.cma.2010.06.011
Cangiani A, Georgoulis EH, Jensen M. Discontinuous Galerkin methods for fast reactive mass transfer through semi-permeable membranes. Appl. Numer. Math. [Internet]. 2016 ;104:3–14. Available from: https://doi.org/10.1016/j.apnum.2014.06.007
Cangiani A, Georgoulis EH, Jensen M. Discontinuous Galerkin methods for mass transfer through semipermeable membranes. SIAM J. Numer. Anal. [Internet]. 2013 ;51:2911–2934. Available from: https://doi.org/10.1137/120890429
Cangiani A, Süli E. Enhanced RFB method. Numer. Math. [Internet]. 2005 ;101:273–308. Available from: https://doi.org/10.1007/s00211-005-0620-7
Cangiani A, Manzini G. Flux reconstruction and solution post-processing in mimetic finite difference methods. Comput. Methods Appl. Mech. Engrg. [Internet]. 2008 ;197:933–945. Available from: https://doi.org/10.1016/j.cma.2007.09.019
Cangiani A, Manzini G, Russo A, Sukumar N. Hourglass stabilization and the virtual element method. Internat. J. Numer. Methods Engrg. [Internet]. 2015 ;102:404–436. Available from: https://doi.org/10.1002/nme.4854
Cangiani A, Manzini G, Russo A, Sukumar N. Hourglass stabilization and the virtual element method. International Journal for Numerical Methods in Engineering [Internet]. 2015 ;102:404-436. Available from: https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.4854
Cangiani A, Georgoulis EH, Giani S, Metcalfe S. hp-adaptive discontinuous Galerkin methods for non-stationary convection–diffusion problems. Computers & Mathematics with Applications [Internet]. 2019 ;78:3090-3104. Available from: https://www.sciencedirect.com/science/article/pii/S0898122119302007
Cangiani A, Dong Z, Georgoulis EH, Houston P. $hp$-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes. ESAIM Math. Model. Numer. Anal. [Internet]. 2016 ;50:699–725. Available from: https://doi.org/10.1051/m2an/2015059
Cangiani A, Georgoulis EH, Houston P. $hp$-version discontinuous Galerkin methods on polygonal and polyhedral meshes. Math. Models Methods Appl. Sci. [Internet]. 2014 ;24:2009–2041. Available from: https://doi.org/10.1142/S0218202514500146
Cangiani A, Dong Z, Georgoulis EH. $hp$-version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes. SIAM J. Sci. Comput. [Internet]. 2017 ;39:A1251–A1279. Available from: https://doi.org/10.1137/16M1073285
Cangiani A, Georgoulis EH, Sabawi M. \it A posteriori error analysis for implicit-explicit $hp$-discontinuous Galerkin timestepping methods for semilinear parabolic problems. J. Sci. Comput. [Internet]. 2020 ;82:Paper No. 26, 24. Available from: https://doi.org/10.1007/s10915-020-01130-2

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