Basarić, Danica; Feireisl, Eduard; Lukáčová-Medvid’ová, Mária; Mizerová, Hana; Yuan, Yuhuan Penalization method for the Navier-Stokes-Fourier system. (English) Zbl 1501.35307 ESAIM, Math. Model. Numer. Anal. 56, No. 6, 1911-1938 (2022). MSC: 35Q35 35A01 76N06 76M12 PDFBibTeX XMLCite \textit{D. Basarić} et al., ESAIM, Math. Model. Numer. Anal. 56, No. 6, 1911--1938 (2022; Zbl 1501.35307) Full Text: DOI arXiv
Lai, Ming-Chih; Chang, Che-Chia; Lin, Wei-Syuan; Hu, Wei-Fan; Lin, Te-Sheng A shallow Ritz method for elliptic problems with singular sources. (English) Zbl 07592144 J. Comput. Phys. 469, Article ID 111547, 14 p. (2022). MSC: 65Nxx 35Jxx 76Mxx PDFBibTeX XMLCite \textit{M.-C. Lai} et al., J. Comput. Phys. 469, Article ID 111547, 14 p. (2022; Zbl 07592144) Full Text: DOI arXiv
Cao, Fujun; Yuan, Dongfang; Sheng, Zhiqiang; Yuan, Guangwei; He, Limin A finite difference method for elliptic problems with implicit jump condition. (English) Zbl 1513.65276 Int. J. Numer. Anal. Model. 19, No. 4, 439-457 (2022). MSC: 65N06 35R35 35J65 PDFBibTeX XMLCite \textit{F. Cao} et al., Int. J. Numer. Anal. Model. 19, No. 4, 439--457 (2022; Zbl 1513.65276) Full Text: Link
Laymuns, Genaro; Sánchez, Manuel A. Corrected finite element methods on unfitted meshes for Stokes moving interface problem. (English) Zbl 1524.65832 Comput. Math. Appl. 108, 159-174 (2022). MSC: 65N30 35J25 65N15 74F10 65N50 76D07 65M60 65M06 92C35 35Q92 74B10 76M10 74S05 35Q35 35Q74 PDFBibTeX XMLCite \textit{G. Laymuns} and \textit{M. A. Sánchez}, Comput. Math. Appl. 108, 159--174 (2022; Zbl 1524.65832) Full Text: DOI
Harikrishnan, B.; Chen, Zhen; Shu, Chang A new explicit immersed boundary method for simulation of fluid-solid interactions. (English) Zbl 1488.35422 Adv. Appl. Math. Mech. 13, No. 2, 261-284 (2021). MSC: 35Q30 76D05 PDFBibTeX XMLCite \textit{B. Harikrishnan} et al., Adv. Appl. Math. Mech. 13, No. 2, 261--284 (2021; Zbl 1488.35422) Full Text: DOI
Kwon, Chunsong; Tartakovsky, Daniel M. Modified immersed boundary method for flows over randomly rough surfaces. (English) Zbl 1453.76035 J. Comput. Phys. 406, Article ID 109195, 16 p. (2020). MSC: 76D05 76M20 35R60 65M06 76D07 PDFBibTeX XMLCite \textit{C. Kwon} and \textit{D. M. Tartakovsky}, J. Comput. Phys. 406, Article ID 109195, 16 p. (2020; Zbl 1453.76035) Full Text: DOI
Chen, Xiaohong; Li, Zhilin; Ruiz Álvarez, Juan A direct IIM approach for two-phase Stokes equations with discontinuous viscosity on staggered grids. (English) Zbl 1410.76281 Comput. Fluids 172, 549-563 (2018). MSC: 76M20 65N06 35Q35 35R05 65N22 76D07 PDFBibTeX XMLCite \textit{X. Chen} et al., Comput. Fluids 172, 549--563 (2018; Zbl 1410.76281) Full Text: DOI
Mittal, H. V. R.; Ray, Rajendra K. Solving immersed interface problems using a new interfacial points-based finite difference approach. (English) Zbl 1448.65195 SIAM J. Sci. Comput. 40, No. 3, A1860-A1883 (2018). MSC: 65N06 52B10 68U05 68U07 65D18 65D05 76M20 76D07 35Q35 35R05 PDFBibTeX XMLCite \textit{H. V. R. Mittal} and \textit{R. K. Ray}, SIAM J. Sci. Comput. 40, No. 3, A1860--A1883 (2018; Zbl 1448.65195) Full Text: DOI
Hosseini, Bamdad; Nigam, Nilima; Stockie, John M. On regularizations of the Dirac delta distribution. (English) Zbl 1349.35008 J. Comput. Phys. 305, 423-447 (2016). MSC: 35A35 35A08 PDFBibTeX XMLCite \textit{B. Hosseini} et al., J. Comput. Phys. 305, 423--447 (2016; Zbl 1349.35008) Full Text: DOI arXiv
Collin, Annabelle; Chapelle, Dominique; Moireau, Philippe A Luenberger observer for reaction-diffusion models with front position data. (English) Zbl 1349.76445 J. Comput. Phys. 300, 288-307 (2015). MSC: 76M20 35K58 35K20 35K57 65M06 94A08 PDFBibTeX XMLCite \textit{A. Collin} et al., J. Comput. Phys. 300, 288--307 (2015; Zbl 1349.76445) Full Text: DOI
Ko, William; Stockie, John M. An immersed boundary model of the cochlea with parametric forcing. (English) Zbl 1316.35031 SIAM J. Appl. Math. 75, No. 3, 1065-1089 (2015). MSC: 35B34 74F10 76D05 76Z05 PDFBibTeX XMLCite \textit{W. Ko} and \textit{J. M. Stockie}, SIAM J. Appl. Math. 75, No. 3, 1065--1089 (2015; Zbl 1316.35031) Full Text: DOI arXiv
Cockburn, Bernardo; Qiu, Weifeng; Solano, Manuel A priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity. (English) Zbl 1290.65110 Math. Comput. 83, No. 286, 665-699 (2014). Reviewer: Petr Sváček (Praha) MSC: 65N30 35J25 65N12 PDFBibTeX XMLCite \textit{B. Cockburn} et al., Math. Comput. 83, No. 286, 665--699 (2014; Zbl 1290.65110) Full Text: DOI
Gibou, Frédéric; Min, Chohong; Fedkiw, Ron High resolution sharp computational methods for elliptic and parabolic problems in complex geometries. (English) Zbl 1263.65093 J. Sci. Comput. 54, No. 2-3, 369-413 (2013). MSC: 65M50 35J05 35K05 80A22 65N50 35R35 65M06 PDFBibTeX XMLCite \textit{F. Gibou} et al., J. Sci. Comput. 54, No. 2--3, 369--413 (2013; Zbl 1263.65093) Full Text: DOI
Araújo, A.; Patrício, F.; Santos, José L. Optimal solution of a reaction–diffusion system with a control discrete source term. (English) Zbl 1210.65150 Int. J. Numer. Methods Biomed. Eng. 27, No. 2, 186-197 (2011). MSC: 65M06 35K57 65K10 65M12 49J20 PDFBibTeX XMLCite \textit{A. Araújo} et al., Int. J. Numer. Methods Biomed. Eng. 27, No. 2, 186--197 (2011; Zbl 1210.65150) Full Text: DOI
Araújo, A.; Patrício, F.; Santos, José L. Optimal solution of a diffusion equation with a discrete source term. (English) Zbl 1204.65100 Int. J. Numer. Methods Biomed. Eng. 26, No. 9, 1176-1187 (2010). Reviewer: Marius Ghergu (Dublin) MSC: 65M06 65M12 35K05 PDFBibTeX XMLCite \textit{A. Araújo} et al., Int. J. Numer. Methods Biomed. Eng. 26, No. 9, 1176--1187 (2010; Zbl 1204.65100) Full Text: DOI Link
Guy, Robert D.; Hartenstine, David A. On the accuracy of direct forcing immersed boundary methods with projection methods. (English) Zbl 1423.76337 J. Comput. Phys. 229, No. 7, 2479-2496 (2010). MSC: 76M25 35Q30 PDFBibTeX XMLCite \textit{R. D. Guy} and \textit{D. A. Hartenstine}, J. Comput. Phys. 229, No. 7, 2479--2496 (2010; Zbl 1423.76337) Full Text: DOI
Chen, Wan; Ward, Michael J. Oscillatory instabilities and dynamics of multi-spike patterns for the one-dimensional Gray-Scott model. (English) Zbl 1197.35021 Eur. J. Appl. Math. 20, No. 2, 187-214 (2009). Reviewer: Denise Huet (Nancy) MSC: 35B25 35K57 80A22 35B32 35Q79 PDFBibTeX XMLCite \textit{W. Chen} and \textit{M. J. Ward}, Eur. J. Appl. Math. 20, No. 2, 187--214 (2009; Zbl 1197.35021) Full Text: DOI
Liu, Hailiang; Wang, Zhongming Superposition of multi-valued solutions in high frequency wave dynamics. (English) Zbl 1203.65141 J. Sci. Comput. 35, No. 2-3, 192-218 (2008). MSC: 65M06 35F20 76M25 PDFBibTeX XMLCite \textit{H. Liu} and \textit{Z. Wang}, J. Sci. Comput. 35, No. 2--3, 192--218 (2008; Zbl 1203.65141) Full Text: DOI
Layton, Anita T. An efficient numerical method for the two-fluid Stokes equations with a moving immersed boundary. (English) Zbl 1158.76381 Comput. Methods Appl. Mech. Eng. 197, No. 25-28, 2147-2155 (2008). MSC: 76M20 76M25 76D07 35R05 65M12 65N06 PDFBibTeX XMLCite \textit{A. T. Layton}, Comput. Methods Appl. Mech. Eng. 197, No. 25--28, 2147--2155 (2008; Zbl 1158.76381) Full Text: DOI
Liang, An; Jing, Xiaodong; Sun, Xiaofeng Constructing spectral schemes of the immersed interface method via a global description of discontinuous functions. (English) Zbl 1147.65098 J. Comput. Phys. 227, No. 18, 8341-8366 (2008). MSC: 65N35 35J25 65N06 65L60 65L12 34B05 PDFBibTeX XMLCite \textit{A. Liang} et al., J. Comput. Phys. 227, No. 18, 8341--8366 (2008; Zbl 1147.65098) Full Text: DOI
Smereka, Peter The numerical approximation of a delta function with application to level set methods. (English) Zbl 1086.65503 J. Comput. Phys. 211, No. 1, 77-90 (2006). MSC: 65D15 65L10 34B05 35J05 65N06 PDFBibTeX XMLCite \textit{P. Smereka}, J. Comput. Phys. 211, No. 1, 77--90 (2006; Zbl 1086.65503) Full Text: DOI
Kandilarov, Juri D.; Vulkov, Lubin G. The immersed interface method for a nonlinear chemical diffusion equation with local sites of reactions. (English) Zbl 1074.65102 Numer. Algorithms 36, No. 4, 285-307 (2004). Reviewer: Marek Brandner (Plzeň) MSC: 65M06 35K57 80A32 80M20 PDFBibTeX XMLCite \textit{J. D. Kandilarov} and \textit{L. G. Vulkov}, Numer. Algorithms 36, No. 4, 285--307 (2004; Zbl 1074.65102) Full Text: DOI
Berthelsen, Petter Andreas A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions. (English) Zbl 1052.65100 J. Comput. Phys. 197, No. 1, 364-386 (2004). MSC: 65N06 35J25 35R05 PDFBibTeX XMLCite \textit{P. A. Berthelsen}, J. Comput. Phys. 197, No. 1, 364--386 (2004; Zbl 1052.65100) Full Text: DOI
Gibou, Frederic; Fedkiw, Ronald P.; Cheng, Li-Tien; Kang, Myungjoo A second-order-accurate symmetric discretization of the Poisson equation on irregular domains. (English) Zbl 0996.65108 J. Comput. Phys. 176, No. 1, 205-227 (2002). MSC: 65N06 65M06 35K05 35R35 35J05 80M20 80A22 PDFBibTeX XMLCite \textit{F. Gibou} et al., J. Comput. Phys. 176, No. 1, 205--227 (2002; Zbl 0996.65108) Full Text: DOI Link
Waldén, Johan On the approximation of singular source terms in differential equations. (English) Zbl 0938.65112 Numer. Methods Partial Differ. Equations 15, No. 4, 503-520 (1999). Reviewer: L.G.Vulkov (Russe) MSC: 65M12 65N12 35R05 35J05 35K05 PDFBibTeX XMLCite \textit{J. Waldén}, Numer. Methods Partial Differ. Equations 15, No. 4, 503--520 (1999; Zbl 0938.65112) Full Text: DOI