Home Research Publications

Books

Polydg A. Cangiani, Z. Dong, E.H. Georgoulis, P. Houston. hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes. SpringerBriefs in Mathematics, Springer, 2017.

BuildingBridges Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations. G. R. Barrenechea, F. Brezzi, A. Cangiani, E.H. Georgoulis (Eds.). Lecture Notes in Computational Science and Engineering, Springer, 2016.

Enumath Numerical Mathematics and Advanced Applications 2011. Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011. A. Cangiani, R. L. Davidchack, E. Georgoulis, A. N. Gorban, J. Levesley, and M. V. Tretyakov editors, Springer, 2013.

Articles

  1. G. Bonnet, A. Cangiani, R. H. Nochetto. Conforming virtual element method for nondivergence form linear elliptic equations with Cordes coefficients. Mathematical Models and Methods in Applied Sciences 35(1), 75--112 2025.

  2. M. Feder, A. Cangiani, and L. Heltai. R3MG: R-tree based agglomeration of polytopal grids with applications to multilevel methods Journal of Computational Physicss 526, 113773, 2025

  3. A. Cangiani, M. Munar, and I. Velásquez. Residual-based a posteriori error estimation for mixed virtual element methods. Computers & Mathematics with Applications, 166, 182--197, 2024

  4. H. Wells, M. E. Hubbard, and A. Cangiani. A Velocity-based Moving Mesh Virtual Element Method. Computers & Mathematics with Applications, 155, 110--125, 2024.

  5. A. Cangiani, Z. Dong, and E. H. Georgoulis. A Posteriori Error Estimates for Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes. SIAM J. on Numer. Anal., 61(5), 2352--2380, 2023

  6. D. Boffi, A. Cangiani, M. Feder, L. Gastaldi, and L. Heltai. A comparison of non-matching techniques for the finite element approximation of interface problems. Computers & Mathematics with Applications, 151, 101--115, 2023

  7. A. Cangiani, Z. Dong, and E. H. Georgoulis. hp-Version discontinuous Galerkin methods on essentially arbitrarily-shaped elements. Mathematics of Computation, 9, 1--35, 2022

  8. N Ferro, S Perotto, and A Cangiani. An Anisotropic Recovery-Based Error Estimator for Adaptive Discontinuous Galerkin Methods. Journal of Scientific Computing, 90(1), 1--24, 2022.

  9. A. Cangiani, E. H. Georgoulis, and O. Sutton. Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods. Mathematical Models and Methods in Applied Sciences, 31(04), 711--751, 2021.

  10. A. Cangiani, E. H. Georgoulis, and M. Sabawi. A posteriori error analysis for implicit-explicit $hp$-discontinuous Galerkin time-stepping methods for semilinear parabolic problems. Journal of Scientific Computing, 82, 26, 2020.

  11. A. Cangiani, E. H. Georgoulis, and Y. Sabawi. Convergence of an adaptive discontinuous Galerkin method for elliptic interface problems. Journal of Computational and Applied Mathematics, 367, 112397, 2020.

  12. A. Cangiani, P. Chatzipantelidis, G. Diwan, and E. H. Georgoulis. Virtual element method for quasilinear elliptic problems. IMA Journal of Numerical Analysis (online), 2019.

  13. A.F. Corno, M.J. Owen, A. Cangiani, and A. Rona. Physiological Fontan Procedure Frontiers in Pediatrics, 7:196, 2019.

  14. A. Cangiani, E. H. Georgoulis, S. Giani, and S. Metcalfe. hp-adaptive discontinuous Galerkin methods for non- stationary convection-diffusion problems. Computers and Mathematics with Applications, 78(9), 3090--3104, 2019.

  15. A. Cangiani, E. H. Georgoulis, A. Yu. Morozov, and O. J. Sutton. Revealing new dynamical patterns in a reaction-diffusion model with cyclic competition via a novel computational framework. Proceedings of the Royal Society A online, 474(2213), 2018.

  16. A. Cangiani, E. H. Georgoulis, and Y. Sabawi. Adaptive discontinuous Galerkin methods for elliptic interface problems. Mathematics of Computation, 87, 2675--2707, 2018.

  17. A. Cangiani, V. Gyrya, G. Manzini, and O. Sutton. Virtual element methods for elliptic problems on polygonal meshes. In: K. Hormann and N. Sukumar, Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics. CRC Press, 2017.

  18. A. Cangiani, Z. Dong, and E. H. Georgoulis. hp-Version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes. SIAM J. Sci. Comput., 39(4), A1251--A1279, 2017.

  19. A. Cangiani, E. H. Georgoulis, T. Pryer, and O. Sutton. A Posteriori Error Estimates for the Virtual Element Method. Numerische Mathematik, 137(4), 857--893, 2017.

  20. A. Cangiani, G. Manzini, and O. Sutton. Conforming and Nonconforming Virtual Element Methods for Elliptic Problems. IMA Journal of Numerical Analysis, 37(3), 1317--1354, 2017.

  21. Paola F. Antonietti, A. Cangiani, J. Collis, Z. Dong, E. H. Georgoulis, S. Giani, and P. Houston. 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. G.R. Barrenechea, F. Brezzi, A. Cangiani, E.H. Georgoulis (Eds.). Lecture Notes in Computational Science and Engineering, Springer, 2016.

  22. A. Cangiani, V. Gyrya, and G. Manzini. The non-conforming Virtual Element Method for the Stokes equations. SIAM J. on Numer. Anal., 54(6), 3411--3435, 2016.

  23. A. Cangiani, E. H. Georgoulis, I. Kyza, and S. Metcalfe. Adaptivity and blow-up detection for nonlinear evolution problems. SIAM J. Sci. Comput., 38(6), 3833--3856, 2016.

  24. A. Cangiani, Z. Dong, E. H. Georgoulis, and P. Houston. hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes. Mathematical Modelling and Numerical Analysis, Vol. 50(3), 699--725, 2016.

  25. A. Cangiani, E. H. Georgoulis, and M. Jensen. Discontinuous Galerkin Methods for Fast Reactive Mass Transfer through Semi-Permeable Membranes. Applied Numerical Mathematics, Vol. 104, 3--14, 2016.

  26. A. Cangiani, G. Manzini, A. Russo, and N. Sukumar. Hourglass stabilization and the virtual element method. International Journal for Numerical Methods in Engineering, Vol. 102(3-4), 404--436, 2015.

  27. A. Cangiani, E. H. Georgoulis, and P. Houston. hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes. Mathematical Models and Methods in Applied Sciences, Vol. 24, No. 10, 2009--2041, 2014.

  28. A. Cangiani, J. Chapman, E. H. Georgoulis, and M. Jensen. On local super-penalization of interior penalty discontinuous Galerkin methods. International Journal of Numerical Analysis and Modeling, Vol. 11(3), 478--495, 2014.

  29. A. Cangiani, E. H. Georgoulis, and S. Metcalfe. An a posteriori error estimator for discontinuous Galerkin methods for non-stationary convection-diffusion problems. IMA Journal of Numerical Analysis, Vol. 34(4), 1578--1597, 2014.

  30. A. Cangiani, J. Chapman, E. H. Georgoulis, and M. Jensen. On the Stability of Continuous-Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems. Journal of Scientific Computing, Vol. 57(2), 313--330, 2013.

  31. A. Cangiani, E. H. Georgoulis, and M. Jensen. Discontinuous Galerkin methods for mass transfer through semi-permeable membranes SIAM J. on Numer. Anal., Vol. 51(5), 2911--2934, 2013.

  32. L. Beirao da Veiga, F. Brezzi, A. Cangiani, G. Manzini, D.L. Marini, and A. Russo. Basic principles of Virtual Element Methods. Mathematical Models and Methods in Applied Sciences, Vol. 23(1), 199--214, 2013.

  33. A. Cangiani, F. Gardini, and G. Manzini. Convergence of the Mimetic Finite Difference Method for eigenvalue problems in mixed form. Computer Methods in Applied Mechanics and Engineering, Vol. 200(9-12), 1150--1160, 2011.

  34. A. Cangiani and R. Natalini. A spatial model of cellular molecular trafficking including active transport along microtubules. Journal of Theoretical Biology, Vol. 267, 614--625, 2010.

  35. A. Cangiani, G. Manzini, and A. Russo. Convergence analysis of the Mimetic Finite Difference Method for elliptic problems. SIAM J. on Numer. Anal., Vol. 47(4), 2612--2637, 2009.

  36. A. Cangiani and G. Manzini. Flux reconstruction and solution post-processing in Mimetic Finite Difference Methods. CMAME, Vol. 197, 933--945, 2008.

  37. A. Cangiani and E. Suli. The Residual-free bubble finite element method on anisotropic partitions. SIAM J. on Numer. Anal., Vol. 45, 1654--1678, 2007.

  38. P. Bagnerini, A. Buffa, and A. Cangiani. A fast algorithm for determining the propagation path of multiply diffracted rays. IEEE Transactions on Antennas and propagation, Vol. 55(5), 1416--1422, 2007.

  39. A. Cangiani and E. Suli. Enhanced RFB Method. Numerische Mathematik, Vol. 101(2), 275--308, 2005.

Conference proceedings

  1. A. Cangiani, J. Chapman, E. H. Georgoulis, and M. Jensen. Implementation of the Continuous-Discontinuous Galerkin Finite Element Method. In: Numerical Mathematics and Advanced Applications 2011. Proceedings of ENUMATH 2011 Conference, Springer, 2013.

  2. A. Cangiani, E. H. Georgoulis, and M. Jensen. Discontinuous Galerkin methods for convection-diffusion problems modelling mass transfer through semipermeable membranes. Proceedings of the Congress on Numerical Methods in Engineering, Coimbra, 2011.

  3. A. Cangiani, E. H. Georgoulis, and M. Jensen. Continuous and discontinuous finite element methods for convection-diffusion problems: a comparison. In G. Lube and G. Rapin, editors, Proceedings of the International Conference on Boundary and Interior Layers (BAIL) - Computational and Asymptotic Methods, 2006.

  4. A. Cangiani and E. Suli. Enhanced residual-free bubble method for convection-diffusion problems. International Journal for Numerical Methods in Fluid, Vol. 47(10-11), 1307--1313, 2005.

Techinical reports

  1. F. Brezzi, A. Cangiani, G. Manzini, and A. Russo. Mimetic Finite Differences and Virtual Element Methods for diffusion problems on polygonal meshes. Technical Report LA-UR-12-22743, Los Alamos National Laboratory, 2012.

  2. A. Cangiani. Biochemical pathways simulation. IAC-CNR Research Report, 2008.

  3. A. Cangiani and E. Suli. A-posteriori error estimators and RFB. Computing Laboratory Technical Report NA-04/22, 2004.

Theses

  1. A. Cangiani. The Residual-Free Bubble Method for Problems with Multiple Scales. Oxford University, DPhil Thesis, 2004.

  2. A. Cangiani. Implied Volatility Estimation using Adjoint Monte Carlo Methods. Oxford University MSc Thesis, 2000

  3. A. Cangiani. Metodi di decomposizione del dominio per le equazioni di Maxwell. Universita di Trento, Tesi di Laurea, 1999.