Open Access
Issue |
ESAIM: M2AN
Volume 57, Number 5, September-October 2023
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Page(s) | 2803 - 2833 | |
DOI | https://doi.org/10.1051/m2an/2023064 | |
Published online | 14 September 2023 |
- S. Badia, F. Verdugo and A.F. Martín, The aggregated unfitted finite element method for elliptic problems. Comput. Methods Appl. Mech. Eng. 336 (2018) 533–553. [CrossRef] [Google Scholar]
- S. Badia, E. Neiva and F. Verdugo, Linking ghost penalty and aggregated unfitted methods. Comput. Methods Appl. Mech. Eng. 388 (2022) 114232. [CrossRef] [Google Scholar]
- P. Bastian and C. Engwer, An unfitted finite element method using discontinuous Galerkin. Int. J. Numer. Methods Eng. 79 (2009) 1557–1576. [Google Scholar]
- T. Belytschko, N. Moes, S. Usui and C. Parimi, Arbitrary discontinuities in finite elements. Int. J. Numer. Methods Eng. 50 (2001) 993–1013. [CrossRef] [Google Scholar]
- S.C. Brenner and L.R. Scott, The mathematical theory of finite element methods. Springer, New York (2008). [CrossRef] [Google Scholar]
- E. Burman, Ghost penalty. C. R. Math. 348 (2010) 1217–1220. [Google Scholar]
- E. Burman and A. Ern, An unfitted hybrid high-order method for elliptic interface problems. SIAM J. Numer. Anal. 56 (2018) 1525–1546. [CrossRef] [MathSciNet] [Google Scholar]
- E. Burman and A. Ern, A cut cell hybrid high-order method for elliptic problems with curved boundaries, edited by F. Radu, K. Kumar, I. Berre, J. Nordbotten and I. Pop. In Numerical Mathematics and Advanced Applications ENUMATH 2017, Lecture Notes in Computational Science and Engineering, Cham, Springer (2017) 173–181. [Google Scholar]
- E. Burman, S. Claus, P. Hansbo, M.G. Larson and A. Massing, CutFEM: Discretizing geometry and partial differential equations. Int. J. Numer. Methods Eng. 104 (2015) 472–501. [Google Scholar]
- E. Burman, P. Hansbo, M.G. Larson and A. Massing, A cut discontinuous Galerkin method for the Laplace-Beltrami operator. IMA J. Numer. Anal. 37 (2017) 138–169. [CrossRef] [MathSciNet] [Google Scholar]
- E. Burman, M. Cicuttin, G. Delay and A. Ern, An unfitted hybrid high-order method with cell agglomeration for elliptic interface problems. SIAM J. Sci. Comput. 43 (2021) A859–A882. [CrossRef] [Google Scholar]
- A. Cangiani, Z. Dong, E.H. Georgoulis and P. Houston, hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes. Springer (2017). [CrossRef] [Google Scholar]
- A. Cangiani, Z. Dong and E. Georgoulis, hp-version discontinuous Galerkin methods on essentially arbitrarily-shaped elements. Math. Comp. 91 (2021) 1–35. [CrossRef] [MathSciNet] [Google Scholar]
- O. Cessenat and B. Despres, Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensional Helmholtz problem. SIAM J. Numer. Anal. 35 (1998) 255–299. [CrossRef] [MathSciNet] [Google Scholar]
- B. Cockburn, J. Gopalakrishnan and R. Lazarov, Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. SIAM J. Numer. Anal. 47 (2009) 1319–1365. [Google Scholar]
- K. Deckelnick, C.M. Elliott and T. Ranner, Unfitted finite element methods using bulk meshes for surface partial differential equations. SIAM J. Numer. Anal. 52 (2014) 2137–2162. [CrossRef] [MathSciNet] [Google Scholar]
- D. Elfverson, M.G. Larson and K. Larsson, CutIGA with basis function removal. Adv. Model. Simul. Eng. Sci. 5 (2018). [CrossRef] [Google Scholar]
- C.M. Elliott and T. Ranner, Finite element analysis for a coupled bulk-surface partial differential equation. IMA J. Numer. Anal. 33 (2012) 377–402. [Google Scholar]
- C. Engwer and F. Heimann, Dune-udg: A cut-cell framework for unfitted discontinuous Galerkin methods. In Advances in DUNE. Springer (2012) 89–100. [CrossRef] [Google Scholar]
- T.P. Fries, S. Omerović, D. Schöllhammer and J. Steidl, Higher-order meshing of implicit geometries—part I: Integration and interpolation in cut elements. Comput. Methods Appl. Mech. Eng. 313 (2017) 759–784. [CrossRef] [Google Scholar]
- C. Gürkan and A. Massing, A stabilized cut discontinuous Galerkin framework for elliptic boundary value and interface problems. Comput. Methods Appl. Mech. Eng. 348 (2019) 466–499. [CrossRef] [Google Scholar]
- C. Gürkan, M. Kronbichler and S. Fernández-Méndez, eXtended hybridizable discontinuous Galerkin with heaviside enrichment for heat bimaterial problems. J. Sci. Comput. 72 (2017) 542–567. [CrossRef] [MathSciNet] [Google Scholar]
- A. Hansbo and P. Hansbo, An unfitted finite element method, based on Nitsche’s method, for elliptic interface problems. Comput. Methods Appl. Mech. Eng. 191 (2002) 5537–5552. [Google Scholar]
- F. Heimann, C. Lehrenfeld, P. Stocker and H. von Wahl, Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems - Reproduction scripts. DOI: 10.5281/zenodo.8020304 (2022). [Google Scholar]
- I. Herrera, Trefftz method, Topics in Boundary Element Research. Springer US (1984) 225–253. [CrossRef] [Google Scholar]
- R. Hiptmair, A. Moiola, I. Perugia and C. Schwab, Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz ℎp-dGFEM. ESAIM Math. Model. Numer. Anal. 48 (2014) 727–752. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods: exponential convergence of the ℎp-version. Found. Comput. Math. 16 (2016) 637–675. [CrossRef] [MathSciNet] [Google Scholar]
- S. Hubrich, P. Di Stolfo, L. Kudela, S. Kollmannsberger, E. Rank, A. Schröder and A. Düster, Numerical integration of discontinuous functions: moment fitting and smart octree. Comput. Mech. 60 (2017) 863–881. [CrossRef] [MathSciNet] [Google Scholar]
- A. Johansson and M.G. Larson, A high order discontinuous Galerkin nitsche method for elliptic problems with fictitious boundary. Numer. Math. 123 (2012) 607–628. [Google Scholar]
- F. Kummer, Extended discontinuous Galerkin methods for two-phase flows: The spatial discretization. Int. J. Numer. Methods Eng. 109 (2017) 259–289. [CrossRef] [Google Scholar]
- M.G. Larson and S. Zahedi, Conservative Discontinuous Cut Finite Element Methods (2021). [Google Scholar]
- C. Lehrenfeld, High order unfitted finite element methods on level set domains using isoparametric mappings. Comput. Methods Appl. Mech. Eng. 300 (2016) 716–733. [Google Scholar]
- C. Lehrenfeld, A higher order isoparametric fictitious domain method for level set domains, edited by S. Bordas, E. Burman, M. Larson and M.A. Olshanskii, Unfitted Finite Element Methods and Applications - Proceedings of the UCL Workshop 2016. In Vol. 121 of Lecture Notes in Computational Science and Engineering, Cham, Springer (2017) 65–92. [CrossRef] [Google Scholar]
- C. Lehrenfeld and A. Reusken, Nitsche-XFEM with streamline diffusion stabilization for a two-phase mass transport problem. SIAM J. Sci. Comp. 34 (2012) 2740–2759. [Google Scholar]
- C. Lehrenfeld and M.A. Olshanskii, An Eulerian finite element method for PDEs in time-dependent domains. ESAIM Math. Model. Numer. Anal. 53 (2019) 585–614. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- C. Lehrenfeld and A. Reusken, Analysis of a high-order unfitted finite element method for elliptic interface problems. IMA J. Numer. Anal. 38 (2017) 1351–1387. [Google Scholar]
- C. Lehrenfeld and A. Stocker, Embedded Trefftz Discontinuous Galerkin Methods (2022). [Google Scholar]
- C. Lehrenfeld, F. Heimann, J. Preuß and H. von Wahl, ngsxfem: Add-on to NGSolve for geometrically unfitted finite element discretizations. J. Open Source Softw. 6 (2021) 3237. [CrossRef] [Google Scholar]
- F. Li, On the negative-order norm accuracy of a local-structure-preserving LDG method. J. Sci. Comput. 51 (2012) 213–223. [CrossRef] [MathSciNet] [Google Scholar]
- F. Li and C.-W. Shu, A local-structure-preserving local discontinuous Galerkin method for the Laplace equation. Methods Appl. Anal. 13 (2006) 215–234. [CrossRef] [MathSciNet] [Google Scholar]
- S. Lu and X. Xu, A Geometrically Consistent Trace Finite Element Method for the Laplace-Beltrami Eigenvalue Problem (2021). [Google Scholar]
- R. Massjung, An unfitted discontinuous Galerkin method applied to elliptic interface problems. SIAM J. Numer. Anal. 50 (2012) 3134–3162. [CrossRef] [MathSciNet] [Google Scholar]
- B. Müller, F. Kummer and M. Oberlack, Highly accurate surface and volume integration on implicit domains by means of moment-fitting. Int. J. Numer. Methods Eng. 96 (2013) 512–528. [Google Scholar]
- N. Moes, J. Dolbow and T. Belytschko, A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46 (1999) 131–150. [CrossRef] [Google Scholar]
- M.A. Olshanskii and D. Safin, Numerical integration over implicitly defined domains for higher order unfitted finite element methods. Lobachevskii J. Math. 37 (2016) 582–596. [CrossRef] [MathSciNet] [Google Scholar]
- J. Parvizian, A. Düster and E. Rank, Finite cell method. Comput. Mech. 41 (2007) 121–133. [CrossRef] [MathSciNet] [Google Scholar]
- A. Poullikkas, A. Karageorghis and G. Georgiou, The method of fundamental solutions for inhomogeneous elliptic problems. Comput. Mech. 22 (1998) 100–107. [CrossRef] [Google Scholar]
- J. Preuß, Higher order unfitted isoparametric space-time FEM on moving domains, Master’s thesis, Georg-August-Universität, Göttingen (2018). [Google Scholar]
- R.I. Saye, High-order quadrature methods for implicitly defined surfaces and volumes in hyperrectangles. SIAM J. Sci. Comput. 37 (2015) A993–A1019. [CrossRef] [Google Scholar]
- J. Schöberl, NETGEN an advancing front 2D/3D-mesh generator based on abstract rules. Comput. Vis. Sci. 1 (1997) 41–52. [CrossRef] [Google Scholar]
- J. Schöberl, C++11 implementation of finite elements in NGSolve. Technical report (2014). [Google Scholar]
- E.M. Stein, Singular integrals and differentiability properties of functions. In Vol. 30 of Princeton Mathematical Series. Princeton University Press, Princeton, NJ (1970). [Google Scholar]
- P. Stocker, NGSTrefftz: Add-on to NGSolve for Trefftz methods. J. Open Source Softw. 7 (2022) 4135. [CrossRef] [Google Scholar]
- E. Trefftz, Ein Gegenstück zum Ritzschen Verfahren. Proc. 2nd Int. Cong. Appl. Mech., Zurich, 1926 (1926) 131–137. [Google Scholar]
- A. Uściłowska-Gajda, J.A. Kołodziej, M. Ciałkowski and A. Frąckowiak, Comparison of two types of Trefftz method for the solution of inhomogeneous elliptic problems. Comput. Assist. Mech. Eng. Sci. 10 (2003) 661–675. [Google Scholar]
- J. Yang, Mi. Potier-Ferry, K. Akpama, H. Hu, Y. Koutsawa, H. Tian and D.S. Zézé, Trefftz methods and Taylor series. Arch. Comput. Methods Eng. 27 (2020) 673–690. [CrossRef] [MathSciNet] [Google Scholar]
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