Di Pietro, Daniele A.; Dong, Zhaonan; Kanschat, Guido; Matalon, Pierre; Rupp, Andreas Homogeneous multigrid for hybrid discretizations: application to HHO methods. arXiv:2403.15858 Preprint, arXiv:2403.15858 [math.NA] (2024). BibTeX Cite \textit{D. A. Di Pietro} et al., ``Homogeneous multigrid for hybrid discretizations: application to HHO methods'', Preprint, arXiv:2403.15858 [math.NA] (2024) Full Text: arXiv OA License
Dong, Zhaonan; Georgoulis, Emmanuil H.; Herbert, Philip J. A hypocoercivity-exploiting stabilised finite element method for Kolmogorov equation. arXiv:2401.12921 Preprint, arXiv:2401.12921 [math.NA] (2024). MSC: 65N30 BibTeX Cite \textit{Z. Dong} et al., ``A hypocoercivity-exploiting stabilised finite element method for Kolmogorov equation'', Preprint, arXiv:2401.12921 [math.NA] (2024) Full Text: arXiv OA License
Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H. A posteriori error estimates for discontinuous Galerkin methods on polygonal and polyhedral meshes. (English) Zbl 1526.65052 SIAM J. Numer. Anal. 61, No. 5, 2352-2380 (2023). Reviewer: Bülent Karasözen (Ankara) MSC: 65N30 65J10 65N15 65N12 65N50 65N85 41A25 PDFBibTeX XMLCite \textit{A. Cangiani} et al., SIAM J. Numer. Anal. 61, No. 5, 2352--2380 (2023; Zbl 1526.65052) Full Text: DOI arXiv
Dong, Zhaonan; Hauck, Moritz; Maier, Roland An improved high-order method for elliptic multiscale problems. (English) Zbl 07725052 SIAM J. Numer. Anal. 61, No. 4, 1918-1937 (2023). MSC: 65N30 65N12 35J30 PDFBibTeX XMLCite \textit{Z. Dong} et al., SIAM J. Numer. Anal. 61, No. 4, 1918--1937 (2023; Zbl 07725052) Full Text: DOI arXiv
Dong, Z.; Mascotto, L. \(hp\)-optimal interior penalty discontinuous Galerkin methods for the biharmonic problem. (English) Zbl 07708372 J. Sci. Comput. 96, No. 1, Paper No. 30, 32 p. (2023). MSC: 65N30 65N50 65N12 65N15 31A30 76D07 35Q35 PDFBibTeX XMLCite \textit{Z. Dong} and \textit{L. Mascotto}, J. Sci. Comput. 96, No. 1, Paper No. 30, 32 p. (2023; Zbl 07708372) Full Text: DOI arXiv
Dong, Zhaonan; Ern, Alexandre; Guermond, Jean-Luc Local decay rates of best-approximation errors using vector-valued finite elements for fields with low regularity and integrable curl or divergence. (English) Zbl 1514.65014 C. R., Math., Acad. Sci. Paris 361, 723-736 (2023). MSC: 65D05 65N30 41A65 PDFBibTeX XMLCite \textit{Z. Dong} et al., C. R., Math., Acad. Sci. Paris 361, 723--736 (2023; Zbl 1514.65014) Full Text: DOI arXiv
Dong, Zhaonan; Mascotto, Lorenzo \(hp\)-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes. arXiv:2310.13564 Preprint, arXiv:2310.13564 [math.NA] (2023). MSC: 65N12 65N30 65N50 BibTeX Cite \textit{Z. Dong} and \textit{L. Mascotto}, ``$hp$-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes'', Preprint, arXiv:2310.13564 [math.NA] (2023) Full Text: arXiv OA License
Dong, Zhaonan; Ern, Alexandre Hybrid high-order and weak Galerkin methods for the biharmonic problem. (English) Zbl 1501.65111 SIAM J. Numer. Anal. 60, No. 5, 2626-2656 (2022). MSC: 65N30 65N15 31A30 74K20 PDFBibTeX XMLCite \textit{Z. Dong} and \textit{A. Ern}, SIAM J. Numer. Anal. 60, No. 5, 2626--2656 (2022; Zbl 1501.65111) Full Text: DOI arXiv
Dong, Zhaonan; Georgoulis, Emmanuil H. Robust interior penalty discontinuous Galerkin methods. (English) Zbl 1502.65197 J. Sci. Comput. 92, No. 2, Paper No. 57, 23 p. (2022). MSC: 65N30 65N15 35J70 PDFBibTeX XMLCite \textit{Z. Dong} and \textit{E. H. Georgoulis}, J. Sci. Comput. 92, No. 2, Paper No. 57, 23 p. (2022; Zbl 1502.65197) Full Text: DOI arXiv
Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H. \(hp\)-version discontinuous Galerkin methods on essentially arbitrarily-shaped elements. (English) Zbl 1484.65295 Math. Comput. 91, No. 333, 1-35 (2022). MSC: 65N30 65N50 65N15 PDFBibTeX XMLCite \textit{A. Cangiani} et al., Math. Comput. 91, No. 333, 1--35 (2022; Zbl 1484.65295) Full Text: DOI arXiv
Dong, Zhaonan; Ern, Alexandre \(C^0\)-hybrid high-order methods for biharmonic problems. arXiv:2206.07074 Preprint, arXiv:2206.07074 [math.NA] (2022). BibTeX Cite \textit{Z. Dong} and \textit{A. Ern}, ``$C^0$-hybrid high-order methods for biharmonic problems'', Preprint, arXiv:2206.07074 [math.NA] (2022) Full Text: arXiv OA License
Dong, Zhaonan; Ern, Alexandre Hybrid high-order method for singularly perturbed fourth-order problems on curved domains. (English) Zbl 1490.65269 ESAIM, Math. Model. Numer. Anal. 55, No. 6, 3091-3114 (2021). MSC: 65N30 65N15 74K20 PDFBibTeX XMLCite \textit{Z. Dong} and \textit{A. Ern}, ESAIM, Math. Model. Numer. Anal. 55, No. 6, 3091--3114 (2021; Zbl 1490.65269) Full Text: DOI arXiv
Dong, Zhaonan; Georgoulis, Emmanuil H.; Kappas, Thomas GPU-accelerated discontinuous Galerkin methods on polytopic meshes. (English) Zbl 1528.65105 SIAM J. Sci. Comput. 43, No. 4, C312-C334 (2021). MSC: 65N30 65Y10 65N50 68Q25 68U05 65R10 PDFBibTeX XMLCite \textit{Z. Dong} et al., SIAM J. Sci. Comput. 43, No. 4, C312--C334 (2021; Zbl 1528.65105) Full Text: DOI arXiv
Dong, Zhaonan; Mascotto, Lorenzo; Sutton, Oliver J. Residual-based a posteriori error estimates for \(hp\)-discontinuous Galerkin discretizations of the biharmonic problem. (English) Zbl 1473.65297 SIAM J. Numer. Anal. 59, No. 3, 1273-1298 (2021). MSC: 65N30 65N12 65N15 65N50 31A30 PDFBibTeX XMLCite \textit{Z. Dong} et al., SIAM J. Numer. Anal. 59, No. 3, 1273--1298 (2021; Zbl 1473.65297) Full Text: DOI arXiv
Dong, Zhaonan; Mascotto, Lorenzo On the suboptimality of the p-version discontinuous Galerkin methods for first order hyperbolic problems. arXiv:2101.03390 Preprint, arXiv:2101.03390 [math.NA] (2021). BibTeX Cite \textit{Z. Dong} and \textit{L. Mascotto}, ``On the suboptimality of the p-version discontinuous Galerkin methods for first order hyperbolic problems'', Preprint, arXiv:2101.03390 [math.NA] (2021) Full Text: arXiv OA License
Dong, Zhaonan; Georgoulis, Emmanuil H.; Pryer, Tristan Recovered finite element methods on polygonal and polyhedral meshes. (English) Zbl 1446.65165 ESAIM, Math. Model. Numer. Anal. 54, No. 4, 1309-1337 (2020). MSC: 65N30 65N50 65N55 35B45 PDFBibTeX XMLCite \textit{Z. Dong} et al., ESAIM, Math. Model. Numer. Anal. 54, No. 4, 1309--1337 (2020; Zbl 1446.65165) Full Text: DOI arXiv Link
Dong, Zhaonan Discontinuous Galerkin methods for the biharmonic problem on polygonal and polyhedral meshes. (English) Zbl 1434.65249 Int. J. Numer. Anal. Model. 16, No. 5, 825-846 (2019). MSC: 65N30 65N50 65N15 31A30 PDFBibTeX XMLCite \textit{Z. Dong}, Int. J. Numer. Anal. Model. 16, No. 5, 825--846 (2019; Zbl 1434.65249) Full Text: arXiv Link
Dong, Zhaonan On the exponent of exponential convergence of \(p\)-version FEM spaces. (English) Zbl 1415.65253 Adv. Comput. Math. 45, No. 2, 757-785 (2019). MSC: 65N30 65N15 65N50 PDFBibTeX XMLCite \textit{Z. Dong}, Adv. Comput. Math. 45, No. 2, 757--785 (2019; Zbl 1415.65253) Full Text: DOI arXiv
Dong, Zhaonan; Georgoulis, Emmanuil H.; Levesley, Jeremy; Usta, Fuat A multilevel sparse kernel-based stochastic collocation finite element method for elliptic problems with random coefficients. (English) Zbl 1442.65365 Comput. Math. Appl. 76, No. 8, 1950-1965 (2018). MSC: 65N30 65N75 35R60 PDFBibTeX XMLCite \textit{Z. Dong} et al., Comput. Math. Appl. 76, No. 8, 1950--1965 (2018; Zbl 1442.65365) Full Text: DOI Link
Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.; Houston, Paul \(hp\)-version discontinuous Galerkin methods on polygonal and polyhedral meshes. (English) Zbl 1382.65307 SpringerBriefs in Mathematics. Cham: Springer (ISBN 978-3-319-67671-5/pbk; 978-3-319-67673-9/ebook). viii, 131 p. (2017). Reviewer: Rolf Dieter Grigorieff (Berlin) MSC: 65M60 65N30 65-02 65M08 65M12 65M15 65M50 65N50 35M12 35J25 35L02 65N12 PDFBibTeX XMLCite \textit{A. Cangiani} et al., \(hp\)-version discontinuous Galerkin methods on polygonal and polyhedral meshes. Cham: Springer (2017; Zbl 1382.65307) Full Text: DOI
Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H. \(hp\)-version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes. (English) Zbl 1371.65106 SIAM J. Sci. Comput. 39, No. 4, A1251-A1279 (2017). MSC: 65M60 35K90 65J08 65M50 65M15 PDFBibTeX XMLCite \textit{A. Cangiani} et al., SIAM J. Sci. Comput. 39, No. 4, A1251--A1279 (2017; Zbl 1371.65106) Full Text: DOI arXiv
Antonietti, Paola F.; Cangiani, Andrea; Collis, Joe; Dong, Zhaonan; Georgoulis, Emmanuil H.; Giani, Stefano; Houston, Paul Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains. (English) Zbl 1357.65251 Barrenechea, Gabriel R. (ed.) et al., Building bridges: connections and challenges in modern approaches to numerical partial differential equations. Selected papers based on the presentations at the 101st LMS-EPSRC symposium, Durham, UK, July 8–16, 2014. Cham: Springer (ISBN 978-3-319-41638-0/hbk; 978-3-319-41640-3/ebook). Lecture Notes in Computational Science and Engineering 114, 281-310 (2016). MSC: 65N30 65N50 65M60 65M50 35J25 35L04 PDFBibTeX XMLCite \textit{P. F. Antonietti} et al., Lect. Notes Comput. Sci. Eng. 114, 281--310 (2016; Zbl 1357.65251) Full Text: DOI Link
Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.; Houston, Paul \(hp\)-version discontinous Gelerkin methods for advection-diffusion-reaction problems on polytropic meshes. (English) Zbl 1342.65213 ESAIM, Math. Model. Numer. Anal. 50, No. 3, 699-725 (2016). Reviewer: Abdallah Bradji (Annaba) MSC: 65N30 65N50 65N55 35J25 PDFBibTeX XMLCite \textit{A. Cangiani} et al., ESAIM, Math. Model. Numer. Anal. 50, No. 3, 699--725 (2016; Zbl 1342.65213) Full Text: DOI
Dong, Z.; Wang, Y. Y. Fixed point characterisation for exact and amenable action. (English) Zbl 1436.43001 Bull. Aust. Math. Soc. 92, No. 2, 228-232 (2015). MSC: 43A07 20F65 43A75 PDFBibTeX XMLCite \textit{Z. Dong} and \textit{Y. Y. Wang}, Bull. Aust. Math. Soc. 92, No. 2, 228--232 (2015; Zbl 1436.43001) Full Text: DOI
Dong, Zhaonan; Georgoulis, Emmanuil H.; Levesley, Jeremy; Usta, Fuat Fast multilevel sparse Gaussian kernels for high-dimensional approximation and integration. arXiv:1501.03296 Preprint, arXiv:1501.03296 [math.NA] (2015). BibTeX Cite \textit{Z. Dong} et al., ``Fast multilevel sparse Gaussian kernels for high-dimensional approximation and integration'', Preprint, arXiv:1501.03296 [math.NA] (2015) Full Text: arXiv OA License
Zhao, Y. F.; Dong, Z. \(p\)-mapping spaces for \(p\)-operator spaces on \(L_{p}\) spaces. (English) Zbl 1336.46051 Ill. J. Math. 58, No. 4, 1071-1091 (2014). Reviewer: Ghadir Sadeghi (Sabzevār) MSC: 46L07 46L06 46L52 PDFBibTeX XMLCite \textit{Y. F. Zhao} and \textit{Z. Dong}, Ill. J. Math. 58, No. 4, 1071--1091 (2014; Zbl 1336.46051) Full Text: Euclid
Dong, Z.; Huang, Ying Finite-representability and \(\mathcal U\)-local reflexivity of operator spaces. (English) Zbl 1232.46054 Houston J. Math. 36, No. 3, 829-842 (2010). Reviewer: Ivan G. Todorov (Belfast) MSC: 46L07 47L25 47L20 PDFBibTeX XMLCite \textit{Z. Dong} and \textit{Y. Huang}, Houston J. Math. 36, No. 3, 829--842 (2010; Zbl 1232.46054) Full Text: Link
Dong, Z. On the local lifting properties of operator spaces. (English) Zbl 1186.46062 Can. J. Math. 61, No. 6, 1262-1278 (2009). MSC: 46L07 47L25 PDFBibTeX XMLCite \textit{Z. Dong}, Can. J. Math. 61, No. 6, 1262--1278 (2009; Zbl 1186.46062) Full Text: DOI
Dong, Z. On the uniqueness of invariant measure of the Burgers equation driven by Lévy processes. (English) Zbl 1148.60038 J. Theor. Probab. 21, No. 2, 322-335 (2008). Reviewer: Andrew Dale (Durban) MSC: 60H20 34F05 PDFBibTeX XMLCite \textit{Z. Dong}, J. Theor. Probab. 21, No. 2, 322--335 (2008; Zbl 1148.60038) Full Text: DOI
Dong, Z. The OLLP and \(\mathcal{T}\)-local reflexivity of operator spaces. (English) Zbl 1155.46025 Ill. J. Math. 51, No. 4, 1103-1122 (2007). MSC: 46L07 PDFBibTeX XMLCite \textit{Z. Dong}, Ill. J. Math. 51, No. 4, 1103--1122 (2007; Zbl 1155.46025) Full Text: Link
Dong, Z. Single elements in some reflexive algebra modules. (English) Zbl 1143.47059 Taiwanese J. Math. 11, No. 1, 107-115 (2007). Reviewer: Maryam Amyari (Mashhad) MSC: 47L75 47C05 47L30 PDFBibTeX XMLCite \textit{Z. Dong}, Taiwanese J. Math. 11, No. 1, 107--115 (2007; Zbl 1143.47059) Full Text: DOI
Hong, Y.; Dong, Z. Genetic algorithms with applications in wireless communications. (English) Zbl 1081.90010 Int. J. Syst. Sci. 35, No. 13-14, 751-762 (2004). MSC: 90B18 90C59 PDFBibTeX XMLCite \textit{Y. Hong} and \textit{Z. Dong}, Int. J. Syst. Sci. 35, No. 13--14, 751--762 (2004; Zbl 1081.90010) Full Text: DOI
Li, C. W.; Dong, Z. On kernel estimations and invariant measures of stochastic jump-diffusions. (English) Zbl 1036.60073 Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 10, No. 1-3, 373-387 (2003). Reviewer: Yana Belopolskaya (St. Petersburg) MSC: 60J75 58J65 PDFBibTeX XMLCite \textit{C. W. Li} and \textit{Z. Dong}, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 10, No. 1--3, 373--387 (2003; Zbl 1036.60073)
Li, C. W.; Dong, Z.; Situ, R. Almost sure stability of linear stochastic differential equations with jumps. (English) Zbl 1019.34055 Probab. Theory Relat. Fields 123, No. 1, 121-155 (2002). Reviewer: Jan Seidler (Praha) MSC: 34D30 93E15 34D08 60F10 28C10 60H10 37H15 60J35 PDFBibTeX XMLCite \textit{C. W. Li} et al., Probab. Theory Relat. Fields 123, No. 1, 121--155 (2002; Zbl 1019.34055) Full Text: DOI
Li, C. W.; Rong, Situ.; Dong, Z. Lyapunov exponents of linear stochastic jump diffusions. (English) Zbl 0966.37023 Fiedler, B. (ed.) et al., International conference on differential equations. Proceedings of the conference, Equadiff ’99, Berlin, Germany, August 1-7, 1999. Vol. 1. Singapore: World Scientific. 133-135 (2000). MSC: 37H15 60G99 37A05 PDFBibTeX XMLCite \textit{C. W. Li} et al., in: International conference on differential equations. Proceedings of the conference, Equadiff '99, Berlin, Germany, August 1--7, 1999. Vol. 1. Singapore: World Scientific. 133--135 (2000; Zbl 0966.37023)