Shu, Chi-Wang Inverse Lax-Wendroff boundary treatment: a survey. (English) Zbl 1524.65395 Commun. Math. Res. 38, No. 3, 333-350 (2022). MSC: 65M06 65M12 65M50 35F30 PDFBibTeX XMLCite \textit{C.-W. Shu}, Commun. Math. Res. 38, No. 3, 333--350 (2022; Zbl 1524.65395) Full Text: DOI
Shu, Chi-Wang Celebrating AWM’s fiftieth anniversary: mentoring PhD students. (English) Zbl 1517.01046 Beery, Janet L. (ed.) et al., Fifty years of women in mathematics. Reminiscences, history, and visions for the future of AWM. Cham: Springer. Assoc. Women Math. Ser. 28, 565-568 (2022). MSC: 01A80 01A74 PDFBibTeX XMLCite \textit{C.-W. Shu}, Assoc. Women Math. Ser. 28, 565--568 (2022; Zbl 1517.01046) Full Text: DOI
Shu, Chi-Wang Essentially non-oscillatory and weighted essentially non-oscillatory schemes. (English) Zbl 07674567 Acta Numerica 29, 701-762 (2020). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{C.-W. Shu}, Acta Numerica 29, 701--762 (2020; Zbl 07674567) Full Text: DOI
Shu, Chi-Wang A class of bound-preserving high order schemes: the main ideas and recent developments. (English) Zbl 1484.65234 Brenner, Susanne C. (ed.) et al., 75 years of mathematics of computation. Symposium celebrating 75 years of mathematics of computation, Institute for Computational and Experimental Research in Mathematics, ICERM, Providence, RI, USA, November 1–3, 2018. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 754, 247-259 (2020). MSC: 65M60 65M06 65N30 65M70 65N35 65D32 76N15 76W05 35B45 35Q31 35Q35 PDFBibTeX XMLCite \textit{C.-W. Shu}, Contemp. Math. 754, 247--259 (2020; Zbl 1484.65234) Full Text: DOI
Shu, Chi-Wang Bound-preserving high-order schemes for hyperbolic equations: survey and recent developments. (English) Zbl 1412.65155 Klingenberg, Christian (ed.) et al., Theory, numerics and applications of hyperbolic problems II, Aachen, Germany, August 2016. Cham: Springer. Springer Proc. Math. Stat. 237, 591-603 (2018). MSC: 65M60 65M08 65M06 35B50 76Y05 35Q31 PDFBibTeX XMLCite \textit{C.-W. Shu}, Springer Proc. Math. Stat. 237, 591--603 (2018; Zbl 1412.65155) Full Text: DOI
Shu, Chi-Wang A brief survey on high order numerical methods for convection dominated problems. (English) Zbl 1380.65182 Lin, Chang-Shou (ed.) et al., Proceedings of the sixth international congress of Chinese mathematicians, ICCM 2013, Taipei, Taiwan, July 14–19, 2013. Volume I. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-348-7/pbk; 978-1-57146-350-0/set). Advanced Lectures in Mathematics (ALM) 36, 119-133 (2017). MSC: 65M06 65M60 65M70 PDFBibTeX XMLCite \textit{C.-W. Shu}, Adv. Lect. Math. (ALM) 36, 119--133 (2017; Zbl 1380.65182)
Shu, Chi-Wang Bound-preserving high order finite volume schemes for conservation laws and convection-diffusion equations. (English) Zbl 1372.65251 Cancès, Clément (ed.) et al., Finite volumes for complex applications VIII – methods and theoretical aspects. FVCA 8, Lille, France, June 12–16, 2017. Cham: Springer (ISBN 978-3-319-57396-0/hbk; 978-3-319-57397-7/ebook; 978-3-319-58818-6/set). Springer Proceedings in Mathematics & Statistics 199, 3-14 (2017). MSC: 65M08 65M12 76M12 PDFBibTeX XMLCite \textit{C.-W. Shu}, Springer Proc. Math. Stat. 199, 3--14 (2017; Zbl 1372.65251) Full Text: DOI
Shu, Chi-Wang Discontinuous Galerkin methods for time-dependent convection dominated problems: basics, recent developments and comparison with other methods. (English) Zbl 1357.65179 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, 371-399 (2016). MSC: 65M60 35L65 35K55 35Q53 65-02 PDFBibTeX XMLCite \textit{C.-W. Shu}, Lect. Notes Comput. Sci. Eng. 114, 371--399 (2016; Zbl 1357.65179) Full Text: DOI
Shu, Chi-Wang Riemann problem and shock capturing schemes. (English) Zbl 1356.65216 Ji, Lizhen (ed.) et al., The legacy of Bernhard Riemann after one hundred and fifty years. Volume II. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-319-7/pbk; 978-1-57146-316-6/set). Advanced Lectures in Mathematics (ALM) 35, 2, 681-689 (2016). MSC: 65M06 35L65 PDFBibTeX XMLCite \textit{C.-W. Shu}, Adv. Lect. Math. (ALM) 35, 681--689 (2016; Zbl 1356.65216)
Shu, Chi-Wang High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments. (English) Zbl 1349.65486 J. Comput. Phys. 316, 598-613 (2016). MSC: 65M60 65M08 65M12 PDFBibTeX XMLCite \textit{C.-W. Shu}, J. Comput. Phys. 316, 598--613 (2016; Zbl 1349.65486) Full Text: DOI
Shu, Chi-Wang Discontinuous Galerkin method for time-dependent convection dominated partial differential equations. (English) Zbl 1388.65107 Jang, Sun Young (ed.) et al., Proceedings of the International Congress of Mathematicians (ICM 2014), Seoul, Korea, August 13–21, 2014. Vol. IV: Invited lectures. Seoul: KM Kyung Moon Sa (ISBN 978-89-6105-807-0/hbk; 978-89-6105-803-2/set). 767-785 (2014). MSC: 65M60 65M20 65M12 65M15 PDFBibTeX XMLCite \textit{C.-W. Shu}, in: Proceedings of the International Congress of Mathematicians (ICM 2014), Seoul, Korea, August 13--21, 2014. Vol. IV: Invited lectures. Seoul: KM Kyung Moon Sa. 767--785 (2014; Zbl 1388.65107)
Shu, Chi-Wang Discontinuous Galerkin method for time-dependent problems: survey and recent developments. (English) Zbl 1282.65122 Feng, Xiaobing (ed.) et al., Recent developments in discontinuous Galerkin finite element methods for partial differential equations. Papers based on the 2012 John H. Barrett memorial lectures, Knoxville, TN, USA, May 9–11, 2012. Cham: Springer (ISBN 978-3-319-01817-1/hbk; 978-3-319-01818-8/ebook). The IMA Volumes in Mathematics and its Applications 157, 25-62 (2014). MSC: 65M60 35L65 65M12 65M15 35F21 35Q53 PDFBibTeX XMLCite \textit{C.-W. Shu}, IMA Vol. Math. Appl. 157, 25--62 (2014; Zbl 1282.65122) Full Text: DOI
Shu, Chi-Wang On high-order accurate weighted essentially non-oscillatory and discontinuous Galerkin schemes for compressible turbulence simulations. (English) Zbl 1353.76039 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 371, No. 1982, Article ID 20120172, 11 p. (2013). MSC: 76F65 65M60 PDFBibTeX XMLCite \textit{C.-W. Shu}, Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 371, No. 1982, Article ID 20120172, 11 p. (2013; Zbl 1353.76039) Full Text: DOI
Shu, Chi-Wang (ed.) Preface. (English) Zbl 1298.00182 Methods Appl. Anal. 20, No. 4, iii-iv (2013). MSC: 00B15 01A70 65-06 PDFBibTeX XMLCite \textit{C.-W. Shu} (ed.), Methods Appl. Anal. 20, No. 4, iii-iv (2013; Zbl 1298.00182) Full Text: Link
Shu, Chi-Wang Survey on discontinuous Galerkin methods for Hamilton-Jacobi equations. (English) Zbl 1278.65157 Li, Jichun (ed.) et al., Recent advances in scientific computing and applications. Eighth international conference on scientific computing and applications, University of Nevada, Las Vegas, NV, USA, April 1–4, 2012. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-8737-0/hbk; 978-0-8218-9501-6/ebook). Contemporary Mathematics 586, 323-330 (2013). MSC: 65M60 PDFBibTeX XMLCite \textit{C.-W. Shu}, Contemp. Math. 586, 323--330 (2013; Zbl 1278.65157) Full Text: DOI
Shu, Chi-Wang Efficient algorithms for solving partial differential equations with discontinuous solutions. (English) Zbl 1253.65155 Notices Am. Math. Soc. 59, No. 5, 615-621 (2012). MSC: 65M60 65M70 35L03 35L60 35Q53 PDFBibTeX XMLCite \textit{C.-W. Shu}, Notices Am. Math. Soc. 59, No. 5, 615--621 (2012; Zbl 1253.65155) Full Text: DOI
Shu, Chi-Wang A brief survey on high order accurate maximum principle satisfying and positivity preserving discontinuous Galerkin and finite volume schemes for conservation laws. (English) Zbl 1247.65130 Ji, Lizhen (ed.) et al., Fifth international congress of Chinese mathematicians. Proceedings of the ICCM ’10, Beijing, China, December 17–22, 2010. Part 2. Providence, RI: American Mathematical Society (AMS); Somerville, MA: International Press (ISBN 978-0-8218-7587-2/pbk; 978-0-8218-7555-1/set). AMS/IP Studies in Advanced Mathematics 51, pt.2, 747-758 (2012). MSC: 65M60 65M08 35L65 76N15 65M12 65M20 35B50 65L06 PDFBibTeX XMLCite \textit{C.-W. Shu}, AMS/IP Stud. Adv. Math. 51, 747--758 (2012; Zbl 1247.65130)
Shu, Chi-Wang High order weighted essentially nonoscillatory schemes for convection dominated problems. (English) Zbl 1160.65330 SIAM Rev. 51, No. 1, 82-126 (2009). MSC: 65M06 35L65 76L05 76M20 85-08 82D37 90B20 92-08 PDFBibTeX XMLCite \textit{C.-W. Shu}, SIAM Rev. 51, No. 1, 82--126 (2009; Zbl 1160.65330) Full Text: DOI Link
Shu, Chi-Wang Discontinuous Galerkin methods for convection dominated partial differential equations. (English) Zbl 1167.65437 Lau, Ka-Sing (ed.) et al., Third international congress of Chinese mathematicians. Part 1. Proceedings of the ICCM ’04, Hong Kong, China, December 17–22, 2004. Providence, RI: American Mathematical Society (AMS); Somerville, MA: International Press (ISBN 978-0-8218-4454-0/pbk; 978-0-8218-4416-8/set). AMS/IP Studies in Advanced Mathematics 42, 1, 63-73 (2008). MSC: 65M60 PDFBibTeX XMLCite \textit{C.-W. Shu}, AMS/IP Stud. Adv. Math. 42, 63--73 (2008; Zbl 1167.65437)
Shu, Chi-Wang An overview on high-order numerical methods for convection-dominated PDEs. (English) Zbl 1062.76037 Hou, Thomas Y. (ed.) et al., Hyperbolic problems: Theory, numerics, applications. Proceedings of the ninth international conference on hyperbolic problems, Pasadena, CA, USA, March 25–29, 2002. Berlin: Springer (ISBN 3-540-44333-9/hbk). 79-88 (2003). MSC: 76M20 76M12 76M10 76R99 76-02 PDFBibTeX XMLCite \textit{C.-W. Shu}, in: Hyperbolic problems: Theory, numerics, applications. Proceedings of the ninth international conference on hyperbolic problems, Pasadena, CA, USA, March 25--29, 2002. Berlin: Springer. 79--88 (2003; Zbl 1062.76037)
Shu, Chi-Wang High-order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD. (English) Zbl 1034.76044 Int. J. Comput. Fluid Dyn. 17, No. 2, 107-118 (2003). MSC: 76M20 76M12 76N15 76-02 PDFBibTeX XMLCite \textit{C.-W. Shu}, Int. J. Comput. Fluid Dyn. 17, No. 2, 107--118 (2003; Zbl 1034.76044) Full Text: DOI
Shu, C.-W. A survey of strong stability preserving high order time discretizations. (English) Zbl 1494.65063 Estep, Donald (ed.) et al., Collected lectures on the preservation of stability under discretization. Lectures presented at the workshop, Colorado State University, Fort Collins, CO, USA, May 30–June 2, 2001. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM). 51-65 (2002). MSC: 65L20 65M20 PDFBibTeX XMLCite \textit{C. W. Shu}, in: Collected lectures on the preservation of stability under discretization. Lectures presented at the workshop, Colorado State University, Fort Collins, CO, USA, May 30--June 2, 2001. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM). 51--65 (2002; Zbl 1494.65063)
Shu, Chi-Wang High order ENO and WENO schemes for computational fluid dynamics. (English) Zbl 0937.76044 Barth, Timothy J. (ed.) et al., High-order methods for computational physics. Berlin: Springer. Lect. Notes Comput. Sci. Eng. 9, 439-582 (1999). MSC: 76M12 76M20 65M06 76N15 PDFBibTeX XMLCite \textit{C.-W. Shu}, Lect. Notes Comput. Sci. Eng. 9, 439--582 (1999; Zbl 0937.76044)
Shu, Chi-Wang Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. (English) Zbl 0927.65111 Quarteroni, Alfio (ed.) et al., Advanced numerical approximation of nonlinear hyperbolic equations. Lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, June 23–28, 1997. Berlin: Springer. Lect. Notes Math. 1697, 325-432 (1998). MSC: 65M06 35L65 65-02 PDFBibTeX XMLCite \textit{C.-W. Shu}, Lect. Notes Math. 1697, 325--432 (1998; Zbl 0927.65111)
Shu, Chi-Wang Essentially non-oscillatory finite difference, finite volume and discontinuous Galerkin finite element methods for conservation laws. (English) Zbl 0843.65069 Bainov, D. (ed.) et al., Proceedings of the third international colloquium on numerical analysis, Plovdiv, Bulgaria, August 13-17, 1994. Utrecht: VSP. 171-180 (1995). MSC: 65M60 65M06 65M12 35L65 PDFBibTeX XMLCite \textit{C.-W. Shu}, in: Proceedings of the third international colloquium on numerical analysis, Plovdiv, Bulgaria, August 13-17, 1994. Utrecht: VSP. 171--180 (1995; Zbl 0843.65069)
Shu, Chi-Wang A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting. (English) Zbl 0757.65098 J. Comput. Phys. 100, No. 2, 424-429 (1992). Reviewer: P.Y.Yalamov (Russe) MSC: 65M06 65M12 35L65 PDFBibTeX XMLCite \textit{C.-W. Shu}, J. Comput. Phys. 100, No. 2, 424--429 (1992; Zbl 0757.65098) Full Text: DOI
Shu, Chi-Wang Numerical experiments on the accuracy of ENO and modified ENO schemes. (English) Zbl 0732.65085 J. Sci. Comput. 5, No. 2, 127-149 (1990). Reviewer: E.Lauckau (Chemnitz) MSC: 65M06 65M12 35L65 PDFBibTeX XMLCite \textit{C.-W. Shu}, J. Sci. Comput. 5, No. 2, 127--149 (1990; Zbl 0732.65085) Full Text: DOI
Shu, Chiwang Total-variation-diminishing time discretizations. (English) Zbl 0662.65081 SIAM J. Sci. Stat. Comput. 9, No. 6, 1073-1084 (1988). Reviewer: H.R.Schwarz MSC: 65M12 65M06 35L65 PDFBibTeX XMLCite \textit{C. Shu}, SIAM J. Sci. Stat. Comput. 9, No. 6, 1073--1084 (1988; Zbl 0662.65081) Full Text: DOI
Shu, Chiwang TVB boundary treatment for numerical solutions of conservation laws. (English) Zbl 0628.65076 Math. Comput. 49, 123-134 (1987). Reviewer: P.K.Mahanti MSC: 65M12 65M06 35L65 PDFBibTeX XMLCite \textit{C. Shu}, Math. Comput. 49, 123--134 (1987; Zbl 0628.65076) Full Text: DOI
Shu, Chiwang TVB uniformly high-order schemes for conservation laws. (English) Zbl 0628.65075 Math. Comput. 49, 105-121 (1987). Reviewer: P.K.Mahanti MSC: 65M12 65M06 35L65 PDFBibTeX XMLCite \textit{C. Shu}, Math. Comput. 49, 105--121 (1987; Zbl 0628.65075) Full Text: DOI