Zhang, Jin; Ma, Xiaoqi Supercloseness of the NIPG method for a singularly perturbed convection diffusion problem on Shishkin mesh. (English) Zbl 07814911 Calcolo 61, No. 1, Paper No. 17, 29 p. (2024). MSC: 65N30 65N12 65N50 65D32 65F35 76R50 PDFBibTeX XMLCite \textit{J. Zhang} and \textit{X. Ma}, Calcolo 61, No. 1, Paper No. 17, 29 p. (2024; Zbl 07814911) Full Text: DOI arXiv
Ma, Xiaoqi; Zhang, Jin Supercloseness of the NIPG method for a singularly perturbed convection diffusion problem on Shishkin mesh in 2D. (English) Zbl 07801653 Comput. Math. Appl. 152, 81-90 (2023). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{X. Ma} and \textit{J. Zhang}, Comput. Math. Appl. 152, 81--90 (2023; Zbl 07801653) Full Text: DOI arXiv
Yadav, Ram Prasad; Rai, Pratima; Sharma, Kapil K. NIPG finite element method for convection-dominated diffusion problems with discontinuous data. (English) Zbl 07714969 Int. J. Comput. Methods 20, No. 5, Article ID 2350001, 25 p. (2023). MSC: 65L11 65L60 65L70 PDFBibTeX XMLCite \textit{R. P. Yadav} et al., Int. J. Comput. Methods 20, No. 5, Article ID 2350001, 25 p. (2023; Zbl 07714969) Full Text: DOI
Rajeev Ranjan, Kumar; Gowrisankar, S. NIPG method on Shishkin mesh for singularly perturbed convection-diffusion problem with discontinuous source term. (English) Zbl 07714952 Int. J. Comput. Methods 20, No. 2, Article ID 2250048, 29 p. (2023). MSC: 65L70 65L20 65L60 PDFBibTeX XMLCite \textit{K. Rajeev Ranjan} and \textit{S. Gowrisankar}, Int. J. Comput. Methods 20, No. 2, Article ID 2250048, 29 p. (2023; Zbl 07714952) Full Text: DOI
Chaturvedi, Abhay Kumar; Chandra Sekhara Rao, S. Analysis of an LDG-FEM for a two-dimensional singularly perturbed convection-reaction-diffusion problem with interior and boundary layers. (English) Zbl 07710408 Appl. Numer. Math. 190, 84-109 (2023). MSC: 65Nxx 65Lxx 65Mxx PDFBibTeX XMLCite \textit{A. K. Chaturvedi} and \textit{S. Chandra Sekhara Rao}, Appl. Numer. Math. 190, 84--109 (2023; Zbl 07710408) Full Text: DOI
Ma, Xiaoqi; Zhang, Jin Supercloseness analysis of the nonsymmetric interior penalty Galerkin method for a singularly perturbed problem on Bakhvalov-type mesh. (English) Zbl 07708920 Appl. Math. Lett. 144, Article ID 108701, 7 p. (2023). MSC: 65Lxx 65Nxx 65Mxx PDFBibTeX XMLCite \textit{X. Ma} and \textit{J. Zhang}, Appl. Math. Lett. 144, Article ID 108701, 7 p. (2023; Zbl 07708920) Full Text: DOI
Cheng, Yao; Stynes, Martin The local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem with characteristic and exponential layers. (English) Zbl 07707128 Numer. Math. 154, No. 1-2, 283-318 (2023). MSC: 65N30 65N50 65N15 35B25 PDFBibTeX XMLCite \textit{Y. Cheng} and \textit{M. Stynes}, Numer. Math. 154, No. 1--2, 283--318 (2023; Zbl 07707128) Full Text: DOI arXiv
Singh, Gautam; Natesan, Srinivasan; Sendur, Ali Superconvergence error analysis of discontinuous Galerkin method with interior penalties for 2D elliptic convection-diffusion-reaction problems. (English) Zbl 1524.65858 Int. J. Comput. Math. 100, No. 5, 948-967 (2023). MSC: 65N30 65N12 65N15 35B25 65D05 35J25 PDFBibTeX XMLCite \textit{G. Singh} et al., Int. J. Comput. Math. 100, No. 5, 948--967 (2023; Zbl 1524.65858) Full Text: DOI
Ulfsby, Tale Bakken; Massing, André; Sticko, Simon Stabilized cut discontinuous Galerkin methods for advection-reaction problems on surfaces. (English) Zbl 07697910 Comput. Methods Appl. Mech. Eng. 413, Article ID 116109, 31 p. (2023). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{T. B. Ulfsby} et al., Comput. Methods Appl. Mech. Eng. 413, Article ID 116109, 31 p. (2023; Zbl 07697910) Full Text: DOI arXiv
Cheng, Yao; Mei, Yanjie Analysis of generalised alternating local discontinuous Galerkin method on layer-adapted mesh for singularly perturbed problems. (English) Zbl 1483.65124 Calcolo 58, No. 4, Paper No. 52, 36 p. (2021). MSC: 65L11 65L20 65L60 PDFBibTeX XMLCite \textit{Y. Cheng} and \textit{Y. Mei}, Calcolo 58, No. 4, Paper No. 52, 36 p. (2021; Zbl 1483.65124) Full Text: DOI
Sharma, Natasha Robust a-posteriori error estimates for weak Galerkin method for the convection-diffusion problem. (English) Zbl 1493.65230 Appl. Numer. Math. 170, 384-397 (2021). MSC: 65N30 65N50 65N15 76R50 PDFBibTeX XMLCite \textit{N. Sharma}, Appl. Numer. Math. 170, 384--397 (2021; Zbl 1493.65230) Full Text: DOI arXiv
Brdar, M.; Radojev, G.; Roos, H.-G.; Teofanov, Lj. Superconvergence analysis of FEM and SDFEM on graded meshes for a problem with characteristic layers. (English) Zbl 1524.65762 Comput. Math. Appl. 93, 50-57 (2021). MSC: 65N30 35J25 65N15 65N12 35B25 PDFBibTeX XMLCite \textit{M. Brdar} et al., Comput. Math. Appl. 93, 50--57 (2021; Zbl 1524.65762) Full Text: DOI arXiv
Zhu, Peng; Xie, Shenglan A uniformly convergent weak Galerkin finite element method on Shishkin mesh for 1d convection-diffusion problem. (English) Zbl 1452.65365 J. Sci. Comput. 85, No. 2, Paper No. 34, 21 p. (2020). MSC: 65N30 65N15 65N12 35B25 65L11 65L60 PDFBibTeX XMLCite \textit{P. Zhu} and \textit{S. Xie}, J. Sci. Comput. 85, No. 2, Paper No. 34, 21 p. (2020; Zbl 1452.65365) Full Text: DOI
Gürkan, Ceren; Sticko, Simon; Massing, André Stabilized cut discontinuous Galerkin methods for advection-reaction problems. (English) Zbl 1451.65191 SIAM J. Sci. Comput. 42, No. 5, A2620-A2654 (2020). MSC: 65N30 65N12 65N15 65N85 PDFBibTeX XMLCite \textit{C. Gürkan} et al., SIAM J. Sci. Comput. 42, No. 5, A2620--A2654 (2020; Zbl 1451.65191) Full Text: DOI arXiv
Bustinza, Rommel; Lombardi, Ariel L.; Solano, Manuel An anisotropic a priori error analysis for a convection-dominated diffusion problem using the HDG method. (English) Zbl 1440.65186 Comput. Methods Appl. Mech. Eng. 345, 382-401 (2019). MSC: 65N30 65N12 65N15 PDFBibTeX XMLCite \textit{R. Bustinza} et al., Comput. Methods Appl. Mech. Eng. 345, 382--401 (2019; Zbl 1440.65186) Full Text: DOI
Singh, Gautam; Natesan, Srinivasan Superconvergence of discontinuous Galerkin method with interior penalties for singularly perturbed two-point boundary-value problems. (English) Zbl 1405.65091 Calcolo 55, No. 4, Paper No. 54, 30 p. (2018). MSC: 65L11 65L20 65L60 65L70 PDFBibTeX XMLCite \textit{G. Singh} and \textit{S. Natesan}, Calcolo 55, No. 4, Paper No. 54, 30 p. (2018; Zbl 1405.65091) Full Text: DOI
Franz, Sebastian; Matthies, Gunar A unified framework for time-dependent singularly perturbed problems with discontinuous Galerkin methods in time. (English) Zbl 1395.65127 Math. Comput. 87, No. 313, 2113-2132 (2018). Reviewer: Aziz Takhirov (Edmonton) MSC: 65N15 35B25 65M12 65M15 65M60 PDFBibTeX XMLCite \textit{S. Franz} and \textit{G. Matthies}, Math. Comput. 87, No. 313, 2113--2132 (2018; Zbl 1395.65127) Full Text: DOI
Zhu, Huiqing; Celiker, Fatih Nodal superconvergence of the local discontinuous Galerkin method for singularly perturbed problems. (English) Zbl 1376.65110 J. Comput. Appl. Math. 330, 95-116 (2018). MSC: 65L20 65L11 34B05 34E15 65L10 65L60 65L50 PDFBibTeX XMLCite \textit{H. Zhu} and \textit{F. Celiker}, J. Comput. Appl. Math. 330, 95--116 (2018; Zbl 1376.65110) Full Text: DOI
Zhang, Jin; Liu, Xiaowei Supercloseness of the SDFEM on Shishkin triangular meshes for problems with exponential layers. (English) Zbl 1377.65153 Adv. Comput. Math. 43, No. 4, 759-775 (2017). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N30 65N12 65N50 35J25 PDFBibTeX XMLCite \textit{J. Zhang} and \textit{X. Liu}, Adv. Comput. Math. 43, No. 4, 759--775 (2017; Zbl 1377.65153) Full Text: DOI arXiv
Chen, Gang; Feng, Minfu; Xie, Xiaoping A robust WG finite element method for convection-diffusion-reaction equations. (English) Zbl 1352.65336 J. Comput. Appl. Math. 315, 107-125 (2017). MSC: 65M60 65N30 PDFBibTeX XMLCite \textit{G. Chen} et al., J. Comput. Appl. Math. 315, 107--125 (2017; Zbl 1352.65336) Full Text: DOI
Yang, Yubo; Zhu, Peng Discontinuous Galerkin methods with interior penalties on graded meshes for 2D singularly perturbed convection-diffusion problems. (English) Zbl 1353.65126 Appl. Numer. Math. 111, 36-48 (2017). MSC: 65N30 35J25 35B25 65N12 65N15 PDFBibTeX XMLCite \textit{Y. Yang} and \textit{P. Zhu}, Appl. Numer. Math. 111, 36--48 (2017; Zbl 1353.65126) Full Text: DOI
Franz, Sebastian Analysis of a family of continuous-discontinuous Galerkin FEM for convection-diffusion problems. (English) Zbl 1351.65089 Appl. Numer. Math. 110, 93-109 (2016). MSC: 65N30 35J25 35B25 65N12 PDFBibTeX XMLCite \textit{S. Franz}, Appl. Numer. Math. 110, 93--109 (2016; Zbl 1351.65089) Full Text: DOI
Jin, Yanyi Local analysis of HDG methods for convection-dominated diffusion problems. (English) Zbl 1337.65140 J. Comput. Appl. Math. 304, 57-72 (2016). MSC: 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{Y. Jin}, J. Comput. Appl. Math. 304, 57--72 (2016; Zbl 1337.65140) Full Text: DOI
Zhu, Peng; Yang, Yubo; Yin, Yunhui Higher order uniformly convergent NIPG methods for 1-d singularly perturbed problems of convection-diffusion type. (English) Zbl 1443.65111 Appl. Math. Modelling 39, No. 22, 6806-6816 (2015). MSC: 65L60 65L11 65L50 PDFBibTeX XMLCite \textit{P. Zhu} et al., Appl. Math. Modelling 39, No. 22, 6806--6816 (2015; Zbl 1443.65111) Full Text: DOI
Cheng, Yao; Zhang, Feng; Zhang, Qiang Local analysis of local discontinuous Galerkin method for the time-dependent singularly perturbed problem. (English) Zbl 1328.65193 J. Sci. Comput. 63, No. 2, 452-477 (2015). MSC: 65M12 65M15 65M60 PDFBibTeX XMLCite \textit{Y. Cheng} et al., J. Sci. Comput. 63, No. 2, 452--477 (2015; Zbl 1328.65193) Full Text: DOI
Fu, Guosheng; Qiu, Weifeng; Zhang, Wujun An analysis of HDG methods for convection-dominated diffusion problems. (English) Zbl 1314.65142 ESAIM, Math. Model. Numer. Anal. 49, No. 1, 225-256 (2015). Reviewer: Qin Meng Zhao (Beijing) MSC: 65N15 65N30 35J47 65N12 PDFBibTeX XMLCite \textit{G. Fu} et al., ESAIM, Math. Model. Numer. Anal. 49, No. 1, 225--256 (2015; Zbl 1314.65142) Full Text: DOI arXiv
Xie, Shenglan; Tu, Huonian; Zhu, Peng Supercloseness result of higher order FEM/LDG coupled method for solving singularly perturbed problem on S-type mesh. (English) Zbl 1470.65146 Abstr. Appl. Anal. 2014, Article ID 260840, 11 p. (2014). MSC: 65L60 34B16 65L11 PDFBibTeX XMLCite \textit{S. Xie} et al., Abstr. Appl. Anal. 2014, Article ID 260840, 11 p. (2014; Zbl 1470.65146) Full Text: DOI
Zhu, Peng; Xie, Shenglan Higher order uniformly convergent continuous/discontinuous Galerkin methods for singularly perturbed problems of convection-diffusion type. (English) Zbl 1288.65156 Appl. Numer. Math. 76, 48-59 (2014). MSC: 65N12 35J25 35B25 65N30 65N50 PDFBibTeX XMLCite \textit{P. Zhu} and \textit{S. Xie}, Appl. Numer. Math. 76, 48--59 (2014; Zbl 1288.65156) Full Text: DOI
Zhu, Huiqing; Zhang, Zhimin Uniform convergence of the LDG method for a singularly perturbed problem with the exponential boundary layer. (English) Zbl 1282.65159 Math. Comput. 83, No. 286, 635-663 (2014). MSC: 65N30 65N12 65N50 35J25 35B25 PDFBibTeX XMLCite \textit{H. Zhu} and \textit{Z. Zhang}, Math. Comput. 83, No. 286, 635--663 (2014; Zbl 1282.65159) Full Text: DOI
Zhu, Huiqing; Zhang, Zhimin Convergence analysis of the LDG method applied to singularly perturbed problems. (English) Zbl 1267.65157 Numer. Methods Partial Differ. Equations 29, No. 2, 396-421 (2013). Reviewer: Yaşar Sözen (Istanbul) MSC: 65N12 65N30 65N50 35B25 35J25 65N15 PDFBibTeX XMLCite \textit{H. Zhu} and \textit{Z. Zhang}, Numer. Methods Partial Differ. Equations 29, No. 2, 396--421 (2013; Zbl 1267.65157) Full Text: DOI
Lombardi, Ariel L.; Pietra, Paola Exponentially fitted discontinuous Galerkin schemes for singularly perturbed problems. (English) Zbl 1251.65161 Numer. Methods Partial Differ. Equations 28, No. 6, 1747-1777 (2012). MSC: 65N30 PDFBibTeX XMLCite \textit{A. L. Lombardi} and \textit{P. Pietra}, Numer. Methods Partial Differ. Equations 28, No. 6, 1747--1777 (2012; Zbl 1251.65161) Full Text: DOI
Zhu, Peng; Xie, Ziqing; Zhou, Shuzi A uniformly convergent continuous-discontinuous Galerkin method for singularly perturbed problems of convection-diffusion type. (English) Zbl 1207.65106 Appl. Math. Comput. 217, No. 9, 4781-4790 (2011). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 65L60 65L10 34B05 34E15 65L20 65L70 PDFBibTeX XMLCite \textit{P. Zhu} et al., Appl. Math. Comput. 217, No. 9, 4781--4790 (2011; Zbl 1207.65106) Full Text: DOI
Zarin, Helena Continuous-discontinuous finite element method for convection-diffusion problems with characteristic layers. (English) Zbl 1193.65204 J. Comput. Appl. Math. 231, No. 2, 626-636 (2009). Reviewer: Răzvan Răducanu (Iaşi) MSC: 65N30 65N12 65N15 35J25 35B25 PDFBibTeX XMLCite \textit{H. Zarin}, J. Comput. Appl. Math. 231, No. 2, 626--636 (2009; Zbl 1193.65204) Full Text: DOI
Lin, Runchang Discontinuous Galerkin least-squares finite element methods for singularly perturbed reaction-diffusion problems with discontinuous coefficients and boundary singularities. (English) Zbl 1163.65087 Numer. Math. 112, No. 2, 295-318 (2009). Reviewer: Răzvan Răducanu (Iaşi) MSC: 65N30 35J25 35B25 35R05 65N15 PDFBibTeX XMLCite \textit{R. Lin}, Numer. Math. 112, No. 2, 295--318 (2009; Zbl 1163.65087) Full Text: DOI