Zhou, Han; Yang, Jiahe; Ying, Wenjun A kernel-free boundary integral method for the nonlinear Poisson-Boltzmann equation. (English) Zbl 07748032 J. Comput. Phys. 493, Article ID 112423, 22 p. (2023). MSC: 65Nxx 35Jxx 65Fxx PDFBibTeX XMLCite \textit{H. Zhou} et al., J. Comput. Phys. 493, Article ID 112423, 22 p. (2023; Zbl 07748032) Full Text: DOI
Xie, Yaning; Li, Shuwang; Ying, Wenjun A fourth-order kernel-free boundary integral method for interface problems. (English) Zbl 1518.65138 Commun. Comput. Phys. 33, No. 3, 764-794 (2023). MSC: 65N38 65N06 65T50 65N22 45K05 35J15 PDFBibTeX XMLCite \textit{Y. Xie} et al., Commun. Comput. Phys. 33, No. 3, 764--794 (2023; Zbl 1518.65138) Full Text: DOI
Ray, Tanushree; Sinha, Rajen Kumar An adaptive immersed finite element method for linear parabolic interface problems with nonzero flux jump. (English) Zbl 1514.35139 Calcolo 60, No. 2, Paper No. 21, 27 p. (2023). MSC: 35J20 65N15 65N30 PDFBibTeX XMLCite \textit{T. Ray} and \textit{R. K. Sinha}, Calcolo 60, No. 2, Paper No. 21, 27 p. (2023; Zbl 1514.35139) Full Text: DOI
Ren, Yiming; Zhao, Shan A FFT accelerated fourth order finite difference method for solving three-dimensional elliptic interface problems. (English) Zbl 07652816 J. Comput. Phys. 477, Article ID 111924, 28 p. (2023). MSC: 65Nxx 35Jxx 35Rxx PDFBibTeX XMLCite \textit{Y. Ren} and \textit{S. Zhao}, J. Comput. Phys. 477, Article ID 111924, 28 p. (2023; Zbl 07652816) Full Text: DOI
Guo, Hailong; Yang, Xu Deep unfitted Nitsche method for elliptic interface problems. (English) Zbl 1493.65203 Commun. Comput. Phys. 31, No. 4, 1162-1179 (2022). MSC: 65N30 68T07 65C05 35J25 35A15 65K05 PDFBibTeX XMLCite \textit{H. Guo} and \textit{X. Yang}, Commun. Comput. Phys. 31, No. 4, 1162--1179 (2022; Zbl 1493.65203) Full Text: DOI arXiv
Jeon, Youngmok An immersed hybrid difference method for the elliptic interface equation. (English) Zbl 1491.65143 Japan J. Ind. Appl. Math. 39, No. 2, 669-692 (2022). Reviewer: Zhen Chao (Milwaukee) MSC: 65N30 65N38 65N50 65N06 35J15 PDFBibTeX XMLCite \textit{Y. Jeon}, Japan J. Ind. Appl. Math. 39, No. 2, 669--692 (2022; Zbl 1491.65143) Full Text: DOI
Guo, Ruchi; Zhang, Xu Solving three-dimensional interface problems with immersed finite elements: a-priori error analysis. (English) Zbl 07513824 J. Comput. Phys. 441, Article ID 110445, 23 p. (2021). MSC: 65Nxx 35Jxx 65Mxx PDFBibTeX XMLCite \textit{R. Guo} and \textit{X. Zhang}, J. Comput. Phys. 441, Article ID 110445, 23 p. (2021; Zbl 07513824) Full Text: DOI arXiv
Pan, Kejia; He, Dongdong; Li, Zhilin A high order compact FD framework for elliptic BVPs involving singular sources, interfaces, and irregular domains. (English) Zbl 1480.65315 J. Sci. Comput. 88, No. 3, Paper No. 67, 25 p. (2021). MSC: 65N06 65N15 65N85 35J15 78A40 35Q60 PDFBibTeX XMLCite \textit{K. Pan} et al., J. Sci. Comput. 88, No. 3, Paper No. 67, 25 p. (2021; Zbl 1480.65315) Full Text: DOI
Han, Yihui; Chen, Huangxin; Wang, Xiao-Ping; Xie, Xiaoping Extended HDG methods for second order elliptic interface problems. (English) Zbl 1452.65339 J. Sci. Comput. 84, No. 1, Paper No. 22, 29 p. (2020). MSC: 65N30 65N15 PDFBibTeX XMLCite \textit{Y. Han} et al., J. Sci. Comput. 84, No. 1, Paper No. 22, 29 p. (2020; Zbl 1452.65339) Full Text: DOI arXiv
Li, Ruo; Yang, Fanyi A discontinuous Galerkin method by patch reconstruction for elliptic interface problem on unfitted mesh. (English) Zbl 1440.65218 SIAM J. Sci. Comput. 42, No. 2, A1428-A1457 (2020). MSC: 65N30 65N12 65N15 PDFBibTeX XMLCite \textit{R. Li} and \textit{F. Yang}, SIAM J. Sci. Comput. 42, No. 2, A1428--A1457 (2020; Zbl 1440.65218) Full Text: DOI arXiv
Schumaker, Larry L. Solving elliptic PDE’s on domains with curved boundaries with an immersed penalized boundary method. (English) Zbl 1428.65094 J. Sci. Comput. 80, No. 3, 1369-1394 (2019). MSC: 65N30 65D07 65N85 35J25 35J05 PDFBibTeX XMLCite \textit{L. L. Schumaker}, J. Sci. Comput. 80, No. 3, 1369--1394 (2019; Zbl 1428.65094) Full Text: DOI
Chen, Xiaohong; Feng, Xiufang; Li, Zhilin A direct method for accurate solution and gradient computations for elliptic interface problems. (English) Zbl 1412.65179 Numer. Algorithms 80, No. 3, 709-740 (2019). MSC: 65N06 65N85 35J25 65K10 PDFBibTeX XMLCite \textit{X. Chen} et al., Numer. Algorithms 80, No. 3, 709--740 (2019; Zbl 1412.65179) Full Text: DOI
Guo, Hailong; Yang, Xu Gradient recovery for elliptic interface problem. I: Body-fitted mesh. (English) Zbl 1488.65615 Commun. Comput. Phys. 23, No. 5, 1488-1511 (2018). MSC: 65N30 35J25 65N12 65N15 65N50 PDFBibTeX XMLCite \textit{H. Guo} and \textit{X. Yang}, Commun. Comput. Phys. 23, No. 5, 1488--1511 (2018; Zbl 1488.65615) Full Text: DOI arXiv
Zhang, Qian; Weng, Zhifeng; Ji, Haifeng; Zhang, Bin Error estimates for an augmented method for one-dimensional elliptic interface problems. (English) Zbl 1448.65203 Adv. Difference Equ. 2018, Paper No. 307, 16 p. (2018). MSC: 65N15 65N30 35J60 82B24 PDFBibTeX XMLCite \textit{Q. Zhang} et al., Adv. Difference Equ. 2018, Paper No. 307, 16 p. (2018; Zbl 1448.65203) Full Text: DOI
Cao, Fujun; Sheng, Zhiqiang; Yuan, Guangwei Monotone finite volume schemes for diffusion equation with imperfect interface on distorted meshes. (English) Zbl 1397.65229 J. Sci. Comput. 76, No. 2, 1055-1077 (2018). MSC: 65N08 65N12 65N50 PDFBibTeX XMLCite \textit{F. Cao} et al., J. Sci. Comput. 76, No. 2, 1055--1077 (2018; Zbl 1397.65229) Full Text: DOI
Hwang, Feng-Nan; Su, Yi-Zhen; Yao, Chien-Chou An iteratively adaptive multiscale finite element method for elliptic interface problems. (English) Zbl 1382.65404 Appl. Numer. Math. 127, 211-225 (2018). MSC: 65N30 35J25 PDFBibTeX XMLCite \textit{F.-N. Hwang} et al., Appl. Numer. Math. 127, 211--225 (2018; Zbl 1382.65404) Full Text: DOI
Guo, Hailong; Yang, Xu Gradient recovery for elliptic interface problem. II: Immersed finite element methods. (English) Zbl 1415.65256 J. Comput. Phys. 338, 606-619 (2017). MSC: 65N30 35J57 35R05 65N15 PDFBibTeX XMLCite \textit{H. Guo} and \textit{X. Yang}, J. Comput. Phys. 338, 606--619 (2017; Zbl 1415.65256) Full Text: DOI arXiv
Chen, Long; Wei, Huayi; Wen, Min An interface-fitted mesh generator and virtual element methods for elliptic interface problems. (English) Zbl 1380.65400 J. Comput. Phys. 334, 327-348 (2017). MSC: 65N50 65N30 35R05 PDFBibTeX XMLCite \textit{L. Chen} et al., J. Comput. Phys. 334, 327--348 (2017; Zbl 1380.65400) Full Text: DOI
Li, Zhilin; Ji, Haifeng; Chen, Xiaohong Accurate solution and gradient computation for elliptic interface problems with variable coefficients. (English) Zbl 1362.76037 SIAM J. Numer. Anal. 55, No. 2, 570-597 (2017). MSC: 76M20 65M06 65M85 PDFBibTeX XMLCite \textit{Z. Li} et al., SIAM J. Numer. Anal. 55, No. 2, 570--597 (2017; Zbl 1362.76037) Full Text: DOI
Mu, Lin; Wang, Junping; Ye, Xiu; Zhao, Shan A new weak Galerkin finite element method for elliptic interface problems. (English) Zbl 1380.65383 J. Comput. Phys. 325, 157-173 (2016). MSC: 65N30 65M12 65M15 PDFBibTeX XMLCite \textit{L. Mu} et al., J. Comput. Phys. 325, 157--173 (2016; Zbl 1380.65383) Full Text: DOI
Xie, Dexuan; Ying, Jinyong A new box iterative method for a class of nonlinear interface problems with application in solving Poisson-Boltzmann equation. (English) Zbl 1348.65170 J. Comput. Appl. Math. 307, 319-334 (2016). MSC: 65N30 65N06 35J60 35Q20 65N55 78A30 78M10 78M20 PDFBibTeX XMLCite \textit{D. Xie} and \textit{J. Ying}, J. Comput. Appl. Math. 307, 319--334 (2016; Zbl 1348.65170) Full Text: DOI
Ji, Haifeng; Chen, Jinru; Li, Zhilin A new augmented immersed finite element method without using SVD interpolations. (English) Zbl 1333.65132 Numer. Algorithms 71, No. 2, 395-416 (2016). MSC: 65N30 35J05 35J25 65F20 35R05 PDFBibTeX XMLCite \textit{H. Ji} et al., Numer. Algorithms 71, No. 2, 395--416 (2016; Zbl 1333.65132) Full Text: DOI
Duan, Huoyuan; Lin, Ping; Tan, Roger C. E. Analysis of a continuous finite element method for \(H(\mathrm{curl},\mathrm{div})\)-elliptic interface problem. (English) Zbl 1268.65151 Numer. Math. 123, No. 4, 671-707 (2013). Reviewer: Pavol Chocholatý (Bratislava) MSC: 65N30 35J25 65N15 PDFBibTeX XMLCite \textit{H. Duan} et al., Numer. Math. 123, No. 4, 671--707 (2013; Zbl 1268.65151) Full Text: DOI
Wu, Chin-Tien; Li, Zhilin; Lai, Ming-Chih Adaptive mesh refinement for elliptic interface problems using the non-conforming immersed finite element method. (English) Zbl 1263.65125 Int. J. Numer. Anal. Model. 8, No. 3, 466-483 (2011). MSC: 65N50 35J25 65N30 65N15 PDFBibTeX XMLCite \textit{C.-T. Wu} et al., Int. J. Numer. Anal. Model. 8, No. 3, 466--483 (2011; Zbl 1263.65125) Full Text: Link
He, Xiaoming; Lin, Tao; Lin, Yanping Interior penalty bilinear IFE discontinuous Galerkin methods for elliptic equations with discontinuous coefficient. (English) Zbl 1205.35010 J. Syst. Sci. Complex. 23, No. 3, 467-483 (2010). Reviewer: Prabhat Kumar Mahanti (Saint John) MSC: 35A35 65N50 35J25 PDFBibTeX XMLCite \textit{X. He} et al., J. Syst. Sci. Complex. 23, No. 3, 467--483 (2010; Zbl 1205.35010) Full Text: DOI
Li, Jingzhi; Melenk, Jens Markus; Wohlmuth, Barbara; Zou, Jun Optimal a priori estimates for higher order finite elements for elliptic interface problems. (English) Zbl 1208.65168 Appl. Numer. Math. 60, No. 1-2, 19-37 (2010). Reviewer: Roland Pulch (Wuppertal) MSC: 65N30 65N12 65N15 35R05 35J25 PDFBibTeX XMLCite \textit{J. Li} et al., Appl. Numer. Math. 60, No. 1--2, 19--37 (2010; Zbl 1208.65168) Full Text: DOI
Jovanović, Boško S.; Vulkov, Lubin G. Finite element approximation of an elliptic boundary value problem with interface. (English) Zbl 1233.65090 Margenov, Svetozar (ed.) et al., Numerical analysis and its applications. 4th international conference, NAA 2008, Lozenetz, Bulgaria, June 16–20, 2008. Revised selected papers. Berlin: Springer (ISBN 978-3-642-00463-6/pbk). Lecture Notes in Computer Science 5434, 56-67 (2009). MSC: 65N30 35J25 PDFBibTeX XMLCite \textit{B. S. Jovanović} and \textit{L. G. Vulkov}, Lect. Notes Comput. Sci. 5434, 56--67 (2009; Zbl 1233.65090) Full Text: DOI