Wang, Hui; Guo, Hui; Zhang, Jiansong; Tian, Lulu Local discontinuous Galerkin methods with decoupled implicit-explicit time marching for the growth-mediated autochemotactic pattern formation model. (English) Zbl 07792922 Adv. Appl. Math. Mech. 16, No. 1, 208-236 (2024). MSC: 65M15 65M60 PDFBibTeX XMLCite \textit{H. Wang} et al., Adv. Appl. Math. Mech. 16, No. 1, 208--236 (2024; Zbl 07792922) Full Text: DOI
Li, Ruo; Yang, Fanyi A reconstructed discontinuous approximation to Monge-Ampère equation in least square formulation. (English) Zbl 1524.65834 Adv. Appl. Math. Mech. 15, No. 5, 1109-1141 (2023). MSC: 65N30 65K10 35J96 65N12 65H10 35J15 PDFBibTeX XMLCite \textit{R. Li} and \textit{F. Yang}, Adv. Appl. Math. Mech. 15, No. 5, 1109--1141 (2023; Zbl 1524.65834) Full Text: DOI arXiv
Zou, Shijun; Yu, Xijun; Dai, Zihuan; Qing, Fang; Zhao, Xiaolong A partial RKDG method for solving the 2D ideal MHD equations written in semi-Lagrangian formulation on moving meshes with exactly divergence-free magnetic field. (English) Zbl 1524.76238 Adv. Appl. Math. Mech. 15, No. 4, 932-963 (2023). MSC: 76M10 76N15 76W05 PDFBibTeX XMLCite \textit{S. Zou} et al., Adv. Appl. Math. Mech. 15, No. 4, 932--963 (2023; Zbl 1524.76238) Full Text: DOI
Li, Shujie; Ju, Lili Unified solution of conjugate fluid and solid heat transfer. I: Solid heat conduction. (English) Zbl 1524.65569 Adv. Appl. Math. Mech. 15, No. 3, 814-830 (2023). MSC: 65M60 65M22 76N06 74F05 74F10 65Y05 80A19 65M06 65N30 65N50 35Q35 PDFBibTeX XMLCite \textit{S. Li} and \textit{L. Ju}, Adv. Appl. Math. Mech. 15, No. 3, 814--830 (2023; Zbl 1524.65569) Full Text: DOI
Zhang, Danni; Guo, Ruihan Optimal error estimates of the semi-discrete local discontinuous Galerkin method and exponential time differencing schemes for the thin film epitaxy problem without slope selection. (English) Zbl 1524.65627 Adv. Appl. Math. Mech. 15, No. 3, 545-567 (2023). MSC: 65M60 35L75 65M06 65N30 65M15 76A20 35R09 35Q35 PDFBibTeX XMLCite \textit{D. Zhang} and \textit{R. Guo}, Adv. Appl. Math. Mech. 15, No. 3, 545--567 (2023; Zbl 1524.65627) Full Text: DOI
Wang, Zhihuan; Gao, Zhen; Wang, Haiyun; Zhang, Qiang; Zhu, Hongqiang Three indication variables and their performance for the troubled-cell indicator using \(K\)-means clustering. (English) Zbl 1513.65389 Adv. Appl. Math. Mech. 15, No. 2, 522-544 (2023). MSC: 65M60 65L06 65N30 35L60 35L65 35L67 PDFBibTeX XMLCite \textit{Z. Wang} et al., Adv. Appl. Math. Mech. 15, No. 2, 522--544 (2023; Zbl 1513.65389) Full Text: DOI
Zhan, Jiajun; Zhong, Liuqiang; Peng, Jie Discontinuous Galerkin methods for semilinear elliptic boundary value problem. (English) Zbl 1513.65475 Adv. Appl. Math. Mech. 15, No. 2, 450-467 (2023). MSC: 65N30 35J61 35B45 65N15 65N12 47J26 PDFBibTeX XMLCite \textit{J. Zhan} et al., Adv. Appl. Math. Mech. 15, No. 2, 450--467 (2023; Zbl 1513.65475) Full Text: DOI arXiv
Li, Di; Liu, Min; Lu, Xiliang; Yang, Jerry Zhijian The discontinuous Galerkin method by patch reconstruction for Helmholtz problems. (English) Zbl 1513.35144 Adv. Appl. Math. Mech. 15, No. 1, 30-48 (2023). MSC: 35J05 65N30 PDFBibTeX XMLCite \textit{D. Li} et al., Adv. Appl. Math. Mech. 15, No. 1, 30--48 (2023; Zbl 1513.35144) Full Text: DOI
Izem, Nouh; Seaid, Mohammed A well-balanced Runge-Kutta discontinuous Galerkin method for multilayer shallow water equations with non-flat bottom topography. (English) Zbl 1499.65496 Adv. Appl. Math. Mech. 14, No. 3, 725-758 (2022). MSC: 65M60 35L65 76B15 86A05 PDFBibTeX XMLCite \textit{N. Izem} and \textit{M. Seaid}, Adv. Appl. Math. Mech. 14, No. 3, 725--758 (2022; Zbl 1499.65496) Full Text: DOI
Gao, Fuzheng; Ye, Xiu; Zhang, Shangyou A discontinuous Galerkin finite element method without interior penalty terms. (English) Zbl 1499.65659 Adv. Appl. Math. Mech. 14, No. 2, 299-314 (2022). MSC: 65N30 65N15 65N12 35J05 PDFBibTeX XMLCite \textit{F. Gao} et al., Adv. Appl. Math. Mech. 14, No. 2, 299--314 (2022; Zbl 1499.65659) Full Text: DOI
Kang, Qiao; Xu, Yan A discontinuous Galerkin method with minimal dissipation for a finite-strain plate. (English) Zbl 1488.65631 Adv. Appl. Math. Mech. 13, No. 5, 1027-1063 (2021). MSC: 65N30 74K20 74B20 65N15 PDFBibTeX XMLCite \textit{Q. Kang} and \textit{Y. Xu}, Adv. Appl. Math. Mech. 13, No. 5, 1027--1063 (2021; Zbl 1488.65631) Full Text: DOI
Li, Jiaojiao; Li, Gang; Qian, Shouguo; Gao, Jinmei; Niu, Qiang A high-order well-balanced discontinuous Galerkin method based on the hydrostatic reconstruction for the Ripa model. (English) Zbl 1488.74133 Adv. Appl. Math. Mech. 12, No. 6, 1416-1437 (2020). MSC: 74S05 PDFBibTeX XMLCite \textit{J. Li} et al., Adv. Appl. Math. Mech. 12, No. 6, 1416--1437 (2020; Zbl 1488.74133) Full Text: DOI
Zhu, Hongqiang; Han, Wenxiu; Wang, Haijin A generalization of a troubled-cell indicator to \(h\)-adaptive meshes for discontinuous Galerkin methods. (English) Zbl 1488.65492 Adv. Appl. Math. Mech. 12, No. 5, 1224-1246 (2020). MSC: 65M60 35L65 65M06 65N30 65L06 65N50 35Q31 35Q53 PDFBibTeX XMLCite \textit{H. Zhu} et al., Adv. Appl. Math. Mech. 12, No. 5, 1224--1246 (2020; Zbl 1488.65492) Full Text: DOI
Sun, Zhiyuan; Liu, Jun; Wang, Pei A discontinuous Galerkin method by patch reconstruction for convection-diffusion problems. (English) Zbl 1488.49064 Adv. Appl. Math. Mech. 12, No. 3, 729-747 (2020). MSC: 49N45 65N21 PDFBibTeX XMLCite \textit{Z. Sun} et al., Adv. Appl. Math. Mech. 12, No. 3, 729--747 (2020; Zbl 1488.49064) Full Text: DOI
Jiang, Kun; Huang, Qiumei; Xu, Xiuxiu Discontinuous Galerkin methods for multi-pantograph delay differential equations. (English) Zbl 1488.65159 Adv. Appl. Math. Mech. 12, No. 1, 189-211 (2020). MSC: 65L03 65L60 65L20 PDFBibTeX XMLCite \textit{K. Jiang} et al., Adv. Appl. Math. Mech. 12, No. 1, 189--211 (2020; Zbl 1488.65159) Full Text: DOI
Zhang, Xiao; Zhang, Yangwen; Singler, John An EDG method for distributed optimal control of elliptic PDEs. (English) Zbl 1488.65678 Adv. Appl. Math. Mech. 10, No. 4, 797-818 (2018). MSC: 65N30 49M25 65N15 PDFBibTeX XMLCite \textit{X. Zhang} et al., Adv. Appl. Math. Mech. 10, No. 4, 797--818 (2018; Zbl 1488.65678) Full Text: DOI arXiv
Yu, Shengjiao; Feng, Renzhong; Yue, Huiqiang; Wang, Zheng; Liu, Tiegang Adjoint-based adaptive isogeometric discontinuous Galerkin method for Euler equations. (English) Zbl 1488.65670 Adv. Appl. Math. Mech. 10, No. 3, 652-672 (2018). MSC: 65N30 76M10 65M15 35Q31 65D07 76N10 76B10 PDFBibTeX XMLCite \textit{S. Yu} et al., Adv. Appl. Math. Mech. 10, No. 3, 652--672 (2018; Zbl 1488.65670) Full Text: DOI
Qin, Wanglong; Cai, Junwei; Lu, Hongqiang; Jimack, Peter K.; Walkley, M. A. A study of preconditioned Jacobian-free Newton-Krylov discontinuous Galerkin method for compressible flows on 3D hexahedral grids. (English) Zbl 1488.65276 Adv. Appl. Math. Mech. 10, No. 2, 261-274 (2018). MSC: 65M06 65M60 65N30 65F08 65F10 76D05 35Q30 PDFBibTeX XMLCite \textit{W. Qin} et al., Adv. Appl. Math. Mech. 10, No. 2, 261--274 (2018; Zbl 1488.65276) Full Text: DOI
Cheng, Jian; Yue, Huiqiang; Yu, Shengjiao; Liu, Tiegang A direct discontinuous Galerkin method with interface correction for the compressible Navier-Stokes equations on unstructured grids. (English) Zbl 1488.65411 Adv. Appl. Math. Mech. 10, No. 1, 1-21 (2018). MSC: 65M60 76N15 65M06 65N30 65F08 65F10 76N06 76M10 76M20 35Q30 PDFBibTeX XMLCite \textit{J. Cheng} et al., Adv. Appl. Math. Mech. 10, No. 1, 1--21 (2018; Zbl 1488.65411) Full Text: DOI
Zhang, Jiansong; Zhu, Jiang; Yang, Danping A combined discontinuous Galerkin method for saltwater intrusion problem with splitting mixed procedure. (English) Zbl 1488.65488 Adv. Appl. Math. Mech. 9, No. 3, 651-666 (2017). MSC: 65M60 65M12 65M15 86A05 76S05 PDFBibTeX XMLCite \textit{J. Zhang} et al., Adv. Appl. Math. Mech. 9, No. 3, 651--666 (2017; Zbl 1488.65488) Full Text: DOI
Lu, Haitian; Zhu, Jun; Wang, Chunwu; Zhao, Ning Runge-Kutta discontinuous Galerkin method with front tracking method for solving the compressible two-medium flow on unstructured meshes. (English) Zbl 1488.65442 Adv. Appl. Math. Mech. 9, No. 1, 73-91 (2017). MSC: 65M60 35L65 65L06 76T10 76T17 76N15 PDFBibTeX XMLCite \textit{H. Lu} et al., Adv. Appl. Math. Mech. 9, No. 1, 73--91 (2017; Zbl 1488.65442) Full Text: DOI Link
Lu, Hongqiang; Cao, Kai; Bian, Lechao; Wu, Yizhao High-order mesh generation for discontinuous Galerkin methods based on elastic deformation. (English) Zbl 1488.65647 Adv. Appl. Math. Mech. 8, No. 4, 693-702 (2016). MSC: 65N30 65N50 74B10 74S05 PDFBibTeX XMLCite \textit{H. Lu} et al., Adv. Appl. Math. Mech. 8, No. 4, 693--702 (2016; Zbl 1488.65647) Full Text: DOI
Zhang, Ya; Nguyen, Duc Duy; Du, Kewei; Xu, Jin; Zhao, Shan Time-domain numerical solutions of Maxwell interface problems with discontinuous electromagnetic waves. (English) Zbl 1488.65318 Adv. Appl. Math. Mech. 8, No. 3, 353-385 (2016). MSC: 65M06 65M60 65M70 65N30 65N35 78M10 78M20 78M22 78A40 35Q61 PDFBibTeX XMLCite \textit{Y. Zhang} et al., Adv. Appl. Math. Mech. 8, No. 3, 353--385 (2016; Zbl 1488.65318) Full Text: DOI Link
Lu, Hongqiang; Xu, Yida; Gao, Yukun; Qin, Wanglong; Sun, Qiang A high-order discontinuous Galerkin method for the two-dimensional time-domain Maxwell’s equations on curved mesh. (English) Zbl 1488.65443 Adv. Appl. Math. Mech. 8, No. 1, 104-116 (2016). MSC: 65M60 78A25 35Q61 PDFBibTeX XMLCite \textit{H. Lu} et al., Adv. Appl. Math. Mech. 8, No. 1, 104--116 (2016; Zbl 1488.65443) Full Text: DOI
Wei, Leilei; He, Yinnian; Zhang, Xindong Analysis of an implicit fully discrete local discontinuous Galerkin method for the time-fractional KdV equation. (English) Zbl 1488.65473 Adv. Appl. Math. Mech. 7, No. 4, 510-527 (2015). MSC: 65M60 65M06 65N30 35K55 65M12 65M15 26A33 35R11 35Q53 PDFBibTeX XMLCite \textit{L. Wei} et al., Adv. Appl. Math. Mech. 7, No. 4, 510--527 (2015; Zbl 1488.65473) Full Text: DOI
Hu, Hongling; Chen, Chuanmiao Superconvergence of bi-\(k\) degree time-space fully discontinuous finite element for first-order hyperbolic equations. (English) Zbl 1488.65421 Adv. Appl. Math. Mech. 7, No. 3, 323-337 (2015). MSC: 65M60 35L04 65M12 PDFBibTeX XMLCite \textit{H. Hu} and \textit{C. Chen}, Adv. Appl. Math. Mech. 7, No. 3, 323--337 (2015; Zbl 1488.65421) Full Text: DOI
Zhu, Hongqiang; Cheng, Yue; Qiu, Jianxian A comparison of the performance of limiters for Runge-Kutta discontinuous Galerkin methods. (English) Zbl 1279.65118 Adv. Appl. Math. Mech. 5, No. 3, 365-390 (2013). MSC: 65M60 35L65 PDFBibTeX XMLCite \textit{H. Zhu} et al., Adv. Appl. Math. Mech. 5, No. 3, 365--390 (2013; Zbl 1279.65118) Full Text: DOI
Yang, Jiming; Xiong, Zhiguang A posteriori error estimates of a combined mixed finite element and discontinuous Galerkin method for a kind of compressible miscible displacement problems. (English) Zbl 1262.65117 Adv. Appl. Math. Mech. 5, No. 2, 163-179 (2013). MSC: 65M12 65M60 PDFBibTeX XMLCite \textit{J. Yang} and \textit{Z. Xiong}, Adv. Appl. Math. Mech. 5, No. 2, 163--179 (2013; Zbl 1262.65117) Full Text: DOI
Karaa, Samir Finite element \(\theta\)-schemes for the acoustic wave equation. (English) Zbl 1262.65131 Adv. Appl. Math. Mech. 3, No. 2, 181-203 (2011). MSC: 65M60 65M12 65M15 PDFBibTeX XMLCite \textit{S. Karaa}, Adv. Appl. Math. Mech. 3, No. 2, 181--203 (2011; Zbl 1262.65131)
Ruas, Vitoriano; De Araujo, José Henrique Carneiro A family of methods of the DG-Morley type for polyharmonic equations. (English) Zbl 1262.65180 Adv. Appl. Math. Mech. 2, No. 3, 303-332 (2010). MSC: 65N30 65N99 76D07 92C55 PDFBibTeX XMLCite \textit{V. Ruas} and \textit{J. H. C. De Araujo}, Adv. Appl. Math. Mech. 2, No. 3, 303--332 (2010; Zbl 1262.65180) Full Text: DOI Link
Li, Jichun A posteriori error estimation for an interior penalty discontinuous Galerkin method for Maxwell’s equations in cold plasma. (English) Zbl 1262.65173 Adv. Appl. Math. Mech. 1, No. 1, 107-124 (2009). MSC: 65N30 35L15 PDFBibTeX XMLCite \textit{J. Li}, Adv. Appl. Math. Mech. 1, No. 1, 107--124 (2009; Zbl 1262.65173)