Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr Finite element methods respecting the discrete maximum principle for convection-diffusion equations. (English) Zbl 07805455 SIAM Rev. 66, No. 1, 3-88 (2024). MSC: 65M60 65M06 65N30 65N50 76R50 35B35 35J05 35B50 35B09 PDFBibTeX XMLCite \textit{G. R. Barrenechea} et al., SIAM Rev. 66, No. 1, 3--88 (2024; Zbl 07805455) Full Text: DOI arXiv
Chen, Jau-Uei; Kang, Shinhoo; Bui-Thanh, Tan; Shadid, John N. A unified hp-HDG framework for Friedrichs’ PDE systems. (English) Zbl 07784362 Comput. Math. Appl. 154, 236-266 (2024). MSC: 65N30 65N15 76M10 65N12 35J25 PDFBibTeX XMLCite \textit{J.-U. Chen} et al., Comput. Math. Appl. 154, 236--266 (2024; Zbl 07784362) Full Text: DOI arXiv
Alnashri, Yahya; Alzubaidi, Hasan Convergence of numerical schemes for convection-diffusion-reaction equations on generic meshes. (English) Zbl 07773381 Results Appl. Math. 19, Article ID 100379, 9 p. (2023). MSC: 65-XX 35K57 65N12 65M08 PDFBibTeX XMLCite \textit{Y. Alnashri} and \textit{H. Alzubaidi}, Results Appl. Math. 19, Article ID 100379, 9 p. (2023; Zbl 07773381) Full Text: DOI
Zhou, Huifang; Liu, Yuanyuan; Sheng, Zhiqiang A finite volume scheme preserving the invariant region property for a class of semilinear parabolic equations on distorted meshes. (English) Zbl 07769117 Numer. Methods Partial Differ. Equations 39, No. 6, 4270-4294 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{H. Zhou} et al., Numer. Methods Partial Differ. Equations 39, No. 6, 4270--4294 (2023; Zbl 07769117) Full Text: DOI
Zhu, Min; Feng, Tingting; Xu, Yong; Cao, Jinde Global dynamics of a dengue fever model incorporating transmission seasonality. (English) Zbl 1519.92328 Nonlinear Anal., Model. Control 28, No. 3, 554-577 (2023). MSC: 92D30 35Q92 PDFBibTeX XMLCite \textit{M. Zhu} et al., Nonlinear Anal., Model. Control 28, No. 3, 554--577 (2023; Zbl 1519.92328) Full Text: DOI
Chang, Kangkang; Zhang, Qimin; Xu, Xinzhong Dynamic behavior of a reaction-diffusion dengue model with spatial heterogeneity. (English) Zbl 1512.35588 Commun. Pure Appl. Anal. 22, No. 3, 751-771 (2023). MSC: 35Q92 92D30 92C60 92-08 37N25 35B40 35B09 35A01 35A02 PDFBibTeX XMLCite \textit{K. Chang} et al., Commun. Pure Appl. Anal. 22, No. 3, 751--771 (2023; Zbl 1512.35588) Full Text: DOI
Zhao, Hongyong; Wang, Kai; Wang, Hao Basic reproduction ratio of a mosquito-borne disease in heterogeneous environment. (English) Zbl 1509.35327 J. Math. Biol. 86, No. 3, Paper No. 32, 51 p. (2023). MSC: 35Q92 92D30 35B35 35B40 35K57 37N25 92-08 PDFBibTeX XMLCite \textit{H. Zhao} et al., J. Math. Biol. 86, No. 3, Paper No. 32, 51 p. (2023; Zbl 1509.35327) Full Text: DOI
Zha, Yijie; Jiang, Weihua Global dynamics and asymptotic profiles for a degenerate dengue fever model in heterogeneous environment. (English) Zbl 1505.92249 J. Differ. Equations 348, 278-319 (2023). MSC: 92D30 35K57 35B35 PDFBibTeX XMLCite \textit{Y. Zha} and \textit{W. Jiang}, J. Differ. Equations 348, 278--319 (2023; Zbl 1505.92249) Full Text: DOI
Zhi, Yuan; Zhan, Huashui The well-posedness problem of an anisotropic porous medium equation with a convection term. (English) Zbl 1509.76092 J. Inequal. Appl. 2022, Paper No. 108, 22 p. (2022). MSC: 76S05 35D30 35B35 PDFBibTeX XMLCite \textit{Y. Zhi} and \textit{H. Zhan}, J. Inequal. Appl. 2022, Paper No. 108, 22 p. (2022; Zbl 1509.76092) Full Text: DOI
Li, Mingshan; Zhao, Hongyong Dynamics of a reaction-diffusion dengue fever model with incubation periods and vertical transmission in heterogeneous environments. (English) Zbl 1504.35584 J. Appl. Math. Comput. 68, No. 6, 3673-3703 (2022). MSC: 35Q92 35B10 35K57 92D30 34B60 PDFBibTeX XMLCite \textit{M. Li} and \textit{H. Zhao}, J. Appl. Math. Comput. 68, No. 6, 3673--3703 (2022; Zbl 1504.35584) Full Text: DOI
Zhu, Min; Liu, Mengli A dengue fever model incorporating heterogeneous cross-diffusion. (Chinese. English summary) Zbl 1513.35250 Acta Math. Sci., Ser. A, Chin. Ed. 42, No. 1, 201-215 (2022). MSC: 35J60 35A01 92D30 PDFBibTeX XMLCite \textit{M. Zhu} and \textit{M. Liu}, Acta Math. Sci., Ser. A, Chin. Ed. 42, No. 1, 201--215 (2022; Zbl 1513.35250) Full Text: Link
Yang, Hongtao; Yu, Boyang; Li, Yonghai; Yuan, Guangwei Monotonicity correction for second order element finite volume methods of anisotropic diffusion problems. (English) Zbl 07524764 J. Comput. Phys. 449, Article ID 110759, 33 p. (2022). MSC: 65Nxx 65Mxx 35Jxx PDFBibTeX XMLCite \textit{H. Yang} et al., J. Comput. Phys. 449, Article ID 110759, 33 p. (2022; Zbl 07524764) Full Text: DOI
Wang, Shuai; Yuan, Guangwei Discrete strong extremum principles for finite element solutions of diffusion problems with nonlinear corrections. (English) Zbl 1483.65193 Appl. Numer. Math. 174, 1-16 (2022). MSC: 65N30 35B50 65N12 35J25 65N50 PDFBibTeX XMLCite \textit{S. Wang} and \textit{G. Yuan}, Appl. Numer. Math. 174, 1--16 (2022; Zbl 1483.65193) Full Text: DOI
Tang, Min; Chang, Lina; Wang, Yihong Tailored finite point method for diffusion equations with interfaces on distorted meshes. (English) Zbl 1501.65090 J. Sci. Comput. 90, No. 1, Paper No. 65, 22 p. (2022). MSC: 65N06 65N50 35J15 35R05 PDFBibTeX XMLCite \textit{M. Tang} et al., J. Sci. Comput. 90, No. 1, Paper No. 65, 22 p. (2022; Zbl 1501.65090) Full Text: DOI
Alnashri, Yahya; Alzubaidi, Hasan A gradient discretisation method for anisotropic reaction-diffusion models with applications to the dynamics of brain tumors. (English) Zbl 07446781 Comput. Methods Appl. Math. 21, No. 4, 753-775 (2021). MSC: 65-XX 35K57 65N12 65M08 PDFBibTeX XMLCite \textit{Y. Alnashri} and \textit{H. Alzubaidi}, Comput. Methods Appl. Math. 21, No. 4, 753--775 (2021; Zbl 07446781) Full Text: DOI arXiv
Wang, Jinliang; Zhang, Ran; Kuniya, Toshikazu A reaction-diffusion susceptible-vaccinated-infected-recovered model in a spatially heterogeneous environment with Dirichlet boundary condition. (English) Zbl 07431548 Math. Comput. Simul. 190, 848-865 (2021). MSC: 35-XX 92-XX PDFBibTeX XMLCite \textit{J. Wang} et al., Math. Comput. Simul. 190, 848--865 (2021; Zbl 07431548) Full Text: DOI
Zhang, Liang; Wang, Shuang-Ming A time-periodic and reaction-diffusion dengue fever model with extrinsic incubation period and crowding effects. (English) Zbl 1430.92118 Nonlinear Anal., Real World Appl. 51, Article ID 102988, 24 p. (2020). MSC: 92D30 35Q92 35K57 PDFBibTeX XMLCite \textit{L. Zhang} and \textit{S.-M. Wang}, Nonlinear Anal., Real World Appl. 51, Article ID 102988, 24 p. (2020; Zbl 1430.92118) Full Text: DOI
Luo, Dongmi; Huang, Weizhang; Qiu, Jianxian A quasi-Lagrangian moving mesh discontinuous Galerkin method for hyperbolic conservation laws. (English) Zbl 1452.65243 J. Comput. Phys. 396, 544-578 (2019). MSC: 65M60 76M10 35L65 65Z05 PDFBibTeX XMLCite \textit{D. Luo} et al., J. Comput. Phys. 396, 544--578 (2019; Zbl 1452.65243) Full Text: DOI arXiv
Zhou, Huifang; Sheng, Zhiqiang; Yuan, Guangwei Physical-bound-preserving finite volume methods for the Nagumo equation on distorted meshes. (English) Zbl 1442.65210 Comput. Math. Appl. 77, No. 4, 1055-1070 (2019). MSC: 65M08 35K20 35K58 92C20 PDFBibTeX XMLCite \textit{H. Zhou} et al., Comput. Math. Appl. 77, No. 4, 1055--1070 (2019; Zbl 1442.65210) Full Text: DOI
Yang, Tinggan; Wang, Yihong A new tailored finite point method for strongly anisotropic diffusion equation on misaligned grids. (English) Zbl 1429.65269 Appl. Math. Comput. 355, 85-95 (2019). MSC: 65N06 35J25 65N12 PDFBibTeX XMLCite \textit{T. Yang} and \textit{Y. Wang}, Appl. Math. Comput. 355, 85--95 (2019; Zbl 1429.65269) Full Text: DOI
Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian Moving mesh finite difference solution of non-equilibrium radiation diffusion equations. (English) Zbl 1434.65170 Numer. Algorithms 82, No. 4, 1409-1440 (2019). Reviewer: Kanakadurga Sivakumar (Chennai) MSC: 65M50 65N06 35Q85 85A25 65L06 65F50 PDFBibTeX XMLCite \textit{X. Yang} et al., Numer. Algorithms 82, No. 4, 1409--1440 (2019; Zbl 1434.65170) Full Text: DOI arXiv
Horváth, Róbert; Faragó, István; Karátson, János Qualitative properties of discrete nonlinear parabolic operators. (English) Zbl 1448.65162 Numer. Math. 143, No. 3, 529-554 (2019). MSC: 65M60 65M22 65N30 65H10 35B50 35K55 PDFBibTeX XMLCite \textit{R. Horváth} et al., Numer. Math. 143, No. 3, 529--554 (2019; Zbl 1448.65162) Full Text: DOI
Wu, Dan; Yue, Jingyan; Yuan, Guangwei; Lv, Junliang Finite volume element approximation for nonlinear diffusion problems with degenerate diffusion coefficients. (English) Zbl 1435.65139 Appl. Numer. Math. 140, 23-47 (2019). MSC: 65M08 35K20 35K65 65M06 PDFBibTeX XMLCite \textit{D. Wu} et al., Appl. Numer. Math. 140, 23--47 (2019; Zbl 1435.65139) Full Text: DOI
Zhou, Huifang; Sheng, Zhiqiang; Yuan, Guangwei Positivity preserving finite volume scheme for the Nagumo-type equations on distorted meshes. (English) Zbl 1427.65213 Appl. Math. Comput. 336, 182-192 (2018). MSC: 65M08 35K20 35K58 92C20 PDFBibTeX XMLCite \textit{H. Zhou} et al., Appl. Math. Comput. 336, 182--192 (2018; Zbl 1427.65213) Full Text: DOI
DiPietro, Kelsey L.; Haynes, Ronald D.; Huang, Weizhang; Lindsay, Alan E.; Yu, Yufei Moving mesh simulation of contact sets in two dimensional models of elastic-electrostatic deflection problems. (English) Zbl 1416.65345 J. Comput. Phys. 375, 763-782 (2018). MSC: 65M60 35K52 65M50 82D80 PDFBibTeX XMLCite \textit{K. L. DiPietro} et al., J. Comput. Phys. 375, 763--782 (2018; Zbl 1416.65345) Full Text: DOI arXiv
Wang, Yihong; Ying, Wenjun; Tang, Min Uniformly convergent scheme for strongly anisotropic diffusion equations with closed field lines. (English) Zbl 1402.65140 SIAM J. Sci. Comput. 40, No. 5, B1253-B1276 (2018). MSC: 65N20 35J75 65N06 35Q79 76X05 PDFBibTeX XMLCite \textit{Y. Wang} et al., SIAM J. Sci. Comput. 40, No. 5, B1253--B1276 (2018; Zbl 1402.65140) Full Text: DOI arXiv
Li, Xianping; Huang, Weizhang A study on nonnegativity preservation in finite element approximation of Nagumo-type nonlinear differential equations. (English) Zbl 1411.65131 Appl. Math. Comput. 309, 49-67 (2017). MSC: 65M60 35K58 92C30 PDFBibTeX XMLCite \textit{X. Li} and \textit{W. Huang}, Appl. Math. Comput. 309, 49--67 (2017; Zbl 1411.65131) Full Text: DOI arXiv
Frittelli, Massimo; Madzvamuse, Anotida; Sgura, Ivonne; Venkataraman, Chandrasekhar Lumped finite elements for reaction-cross-diffusion systems on stationary surfaces. (English) Zbl 1397.65185 Comput. Math. Appl. 74, No. 12, 3008-3023 (2017). MSC: 65M60 35K51 35K57 35K58 65M06 65M15 65M12 PDFBibTeX XMLCite \textit{M. Frittelli} et al., Comput. Math. Appl. 74, No. 12, 3008--3023 (2017; Zbl 1397.65185) Full Text: DOI arXiv
Huang, Weizhang Sign-preserving of principal eigenfunctions in P1 finite element approximation of eigenvalue problems of second-order elliptic operators. (English) Zbl 1352.65511 J. Comput. Phys. 274, 230-244 (2014). MSC: 65N30 65N25 35J25 35P05 PDFBibTeX XMLCite \textit{W. Huang}, J. Comput. Phys. 274, 230--244 (2014; Zbl 1352.65511) Full Text: DOI arXiv
Kamenski, Lennard; Huang, Weizhang; Xu, Hongguo Conditioning of finite element equations with arbitrary anisotropic meshes. (English) Zbl 1303.65097 Math. Comput. 83, No. 289, 2187-2211 (2014). Reviewer: Ivan Secrieru (Chişinău) MSC: 65N30 65F35 35J25 65N50 PDFBibTeX XMLCite \textit{L. Kamenski} et al., Math. Comput. 83, No. 289, 2187--2211 (2014; Zbl 1303.65097) Full Text: DOI arXiv
Lu, Changna; Huang, Weizhang; Qiu, Jianxian Maximum principle in linear finite element approximations of anisotropic diffusion-convection-reaction problems. (English) Zbl 1300.65088 Numer. Math. 127, No. 3, 515-537 (2014). Reviewer: Tomas Vejchodsky (Praha) MSC: 65N30 65N50 35B50 35J25 PDFBibTeX XMLCite \textit{C. Lu} et al., Numer. Math. 127, No. 3, 515--537 (2014; Zbl 1300.65088) Full Text: DOI arXiv
Kreuzer, Christian A note on why enforcing discrete maximum principles by a simple a posteriori cutoff is a good idea. (English) Zbl 1290.65114 Numer. Methods Partial Differ. Equations 30, No. 3, 994-1002 (2014). MSC: 65N30 35J92 35B50 PDFBibTeX XMLCite \textit{C. Kreuzer}, Numer. Methods Partial Differ. Equations 30, No. 3, 994--1002 (2014; Zbl 1290.65114) Full Text: DOI arXiv
Lu, Changna; Huang, Weizhang; Van Vleck, Erik S. The cutoff method for the numerical computation of nonnegative solutions of parabolic PDEs with application to anisotropic diffusion and lubrication-type equations. (English) Zbl 1297.65097 J. Comput. Phys. 242, 24-36 (2013). MSC: 65M06 35K55 65M12 35K20 PDFBibTeX XMLCite \textit{C. Lu} et al., J. Comput. Phys. 242, 24--36 (2013; Zbl 1297.65097) Full Text: DOI arXiv
Li, Xianping; Huang, Weizhang Maximum principle for the finite element solution of time-dependent anisotropic diffusion problems. (English) Zbl 1307.65134 Numer. Methods Partial Differ. Equations 29, No. 6, 1963-1985 (2013). Reviewer: Weizhong Dai (Ruston) MSC: 65M60 65M12 35K20 35B50 65M06 PDFBibTeX XMLCite \textit{X. Li} and \textit{W. Huang}, Numer. Methods Partial Differ. Equations 29, No. 6, 1963--1985 (2013; Zbl 1307.65134) Full Text: DOI arXiv