Burkardt, John; Pei, Wenlong; Trenchea, Catalin A stress test for the midpoint time-stepping method. (English) Zbl 1490.65134 Int. J. Numer. Anal. Model. 19, No. 2-3, 299-314 (2022). MSC: 65L05 34D20 35L65 65C20 65D30 65L07 65L20 65M12 PDFBibTeX XMLCite \textit{J. Burkardt} et al., Int. J. Numer. Anal. Model. 19, No. 2--3, 299--314 (2022; Zbl 1490.65134) Full Text: Link
Burkardt, John; Wu, Yixuan; Zhang, Yanzhi A unified meshfree pseudospectral method for solving both classical and fractional PDEs. (English) Zbl 1471.65207 SIAM J. Sci. Comput. 43, No. 2, A1389-A1411 (2021). MSC: 65N35 65D12 65R20 41A05 35R11 PDFBibTeX XMLCite \textit{J. Burkardt} et al., SIAM J. Sci. Comput. 43, No. 2, A1389--A1411 (2021; Zbl 1471.65207) Full Text: DOI arXiv
Burkardt, John; Gunzburger, Max; Zhao, Wenju High-precision computation of the weak Galerkin methods for the fourth-order problem. (English) Zbl 1434.65238 Numer. Algorithms 84, No. 1, 181-205 (2020). MSC: 65N30 35J30 PDFBibTeX XMLCite \textit{J. Burkardt} et al., Numer. Algorithms 84, No. 1, 181--205 (2020; Zbl 1434.65238) Full Text: DOI
Xu, Feifei; Gunzburger, Max; Burkardt, John A multiscale method for nonlocal mechanics and diffusion and for the approximation of discontinuous functions. (English) Zbl 1436.74076 Comput. Methods Appl. Mech. Eng. 307, 117-143 (2016). MSC: 74S05 65N30 74A05 PDFBibTeX XMLCite \textit{F. Xu} et al., Comput. Methods Appl. Mech. Eng. 307, 117--143 (2016; Zbl 1436.74076) Full Text: DOI
Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max; Burkardt, John Hyperspherical sparse approximation techniques for high-dimensional discontinuity detection. (English) Zbl 1386.65083 SIAM Rev. 58, No. 3, 517-551 (2016). MSC: 65D15 PDFBibTeX XMLCite \textit{G. Zhang} et al., SIAM Rev. 58, No. 3, 517--551 (2016; Zbl 1386.65083) Full Text: DOI
Xu, Feifei; Gunzburger, Max; Burkardt, John; Du, Qiang A multiscale implementation based on adaptive mesh refinement for the nonlocal peridynamics model in one dimension. (English) Zbl 1381.74214 Multiscale Model. Simul. 14, No. 1, 398-429 (2016). MSC: 74S05 65R20 35Q74 45B05 74A45 74A99 65N30 45E05 PDFBibTeX XMLCite \textit{F. Xu} et al., Multiscale Model. Simul. 14, No. 1, 398--429 (2016; Zbl 1381.74214) Full Text: DOI
Zhang, G.; Webster, C.; Gunzburger, M.; Burkardt, J. A hyperspherical adaptive sparse-grid method for high-dimensional discontinuity detection. (English) Zbl 1317.65058 SIAM J. Numer. Anal. 53, No. 3, 1508-1536 (2015). MSC: 65D15 PDFBibTeX XMLCite \textit{G. Zhang} et al., SIAM J. Numer. Anal. 53, No. 3, 1508--1536 (2015; Zbl 1317.65058) Full Text: DOI Link
Nguyen, Hoa; Gunzburger, Max; Ju, Lili; Burkardt, John Adaptive anisotropic meshing for steady convection-dominated problems. (English) Zbl 1229.76055 Comput. Methods Appl. Mech. Eng. 198, No. 37-40, 2964-2981 (2009). MSC: 76M10 76R99 PDFBibTeX XMLCite \textit{H. Nguyen} et al., Comput. Methods Appl. Mech. Eng. 198, No. 37--40, 2964--2981 (2009; Zbl 1229.76055) Full Text: DOI Link
Nguyen, Hoa; Burkardt, John; Gunzburger, Max; Ju, Lili; Saka, Yuki Constrained CVT meshes and a comparison of triangular mesh generators. (English) Zbl 1152.65035 Comput. Geom. 42, No. 1, 1-19 (2009). MSC: 65D18 65N50 65N30 PDFBibTeX XMLCite \textit{H. Nguyen} et al., Comput. Geom. 42, No. 1, 1--19 (2009; Zbl 1152.65035) Full Text: DOI Link
Burkardt, John; Gunzburger, Max; Lee, Hyung-Chun POD and CVT-based reduced-order modeling of Navier-Stokes flows. (English) Zbl 1120.76323 Comput. Methods Appl. Mech. Eng. 196, No. 1-3, 337-355 (2006). MSC: 76M10 76D05 PDFBibTeX XMLCite \textit{J. Burkardt} et al., Comput. Methods Appl. Mech. Eng. 196, No. 1--3, 337--355 (2006; Zbl 1120.76323) Full Text: DOI
Burkardt, John; Gunzburger, Max; Peterson, Janet Insensitive functionals, inconsistent gradients, spurious minima, and regularized functionals in flow optimization problems. (English) Zbl 1003.76023 Int. J. Comput. Fluid Dyn. 16, No. 3, 171-185 (2002). MSC: 76D55 76M20 PDFBibTeX XMLCite \textit{J. Burkardt} et al., Int. J. Comput. Fluid Dyn. 16, No. 3, 171--185 (2002; Zbl 1003.76023) Full Text: DOI