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Tailored finite point method for the interface problem
1.  Dept. of Mathematical Sciences, Tsinghua University, Beijing 100084 
[1] 
Sheng Xu. Derivation of principal jump conditions for the immersed interface method in twofluid flow simulation. Conference Publications, 2009, 2009 (Special) : 838845. doi: 10.3934/proc.2009.2009.838 
[2] 
Hongsong Feng, Shan Zhao. A multigrid based finite difference method for solving parabolic interface problem. Electronic Research Archive, 2021, 29 (5) : 31413170. doi: 10.3934/era.2021031 
[3] 
Thierry Horsin, Peter I. Kogut, Olivier Wilk. Optimal $L^2$control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions. Mathematical Control and Related Fields, 2016, 6 (4) : 595628. doi: 10.3934/mcrf.2016017 
[4] 
Lunji Song, Wenya Qi, Kaifang Liu, Qingxian Gu. A new overpenalized weak galerkin finite element method. Part Ⅱ: Elliptic interface problems. Discrete and Continuous Dynamical Systems  B, 2021, 26 (5) : 25812598. doi: 10.3934/dcdsb.2020196 
[5] 
Elena Kosygina. Brownian flow on a finite interval with jump boundary conditions. Discrete and Continuous Dynamical Systems  B, 2006, 6 (4) : 867880. doi: 10.3934/dcdsb.2006.6.867 
[6] 
Peter I. Kogut. On approximation of an optimal boundary control problem for linear elliptic equation with unbounded coefficients. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 21052133. doi: 10.3934/dcds.2014.34.2105 
[7] 
Hugo Beirão da Veiga. A challenging open problem: The inviscid limit under sliptype boundary conditions.. Discrete and Continuous Dynamical Systems  S, 2010, 3 (2) : 231236. doi: 10.3934/dcdss.2010.3.231 
[8] 
Runchang Lin, Huiqing Zhu. A discontinuous Galerkin leastsquares finite element method for solving Fisher's equation. Conference Publications, 2013, 2013 (special) : 489497. doi: 10.3934/proc.2013.2013.489 
[9] 
Pierpaolo Soravia. Uniqueness results for fully nonlinear degenerate elliptic equations with discontinuous coefficients. Communications on Pure and Applied Analysis, 2006, 5 (1) : 213240. doi: 10.3934/cpaa.2006.5.213 
[10] 
Sofia Giuffrè, Giovanna Idone. On linear and nonlinear elliptic boundary value problems in the plane with discontinuous coefficients. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 13471363. doi: 10.3934/dcds.2011.31.1347 
[11] 
Feng Zhou, Zhenqiu Zhang. Pointwise gradient estimates for subquadratic elliptic systems with discontinuous coefficients. Communications on Pure and Applied Analysis, 2019, 18 (6) : 31373160. doi: 10.3934/cpaa.2019141 
[12] 
Christos V. Nikolopoulos, Georgios E. Zouraris. Numerical solution of a nonlocal elliptic problem modeling a thermistor with a finite element and a finite volume method. Conference Publications, 2007, 2007 (Special) : 768778. doi: 10.3934/proc.2007.2007.768 
[13] 
Champike Attanayake, SoHsiang Chou. An immersed interface method for Pennes bioheat transfer equation. Discrete and Continuous Dynamical Systems  B, 2015, 20 (2) : 323337. doi: 10.3934/dcdsb.2015.20.323 
[14] 
SoHsiang Chou. An immersed linear finite element method with interface flux capturing recovery. Discrete and Continuous Dynamical Systems  B, 2012, 17 (7) : 23432357. doi: 10.3934/dcdsb.2012.17.2343 
[15] 
Thierry Horsin, Peter I. Kogut. Optimal $L^2$control problem in coefficients for a linear elliptic equation. I. Existence result. Mathematical Control and Related Fields, 2015, 5 (1) : 7396. doi: 10.3934/mcrf.2015.5.73 
[16] 
Dongsheng Yin, Min Tang, Shi Jin. The Gaussian beam method for the wigner equation with discontinuous potentials. Inverse Problems and Imaging, 2013, 7 (3) : 10511074. doi: 10.3934/ipi.2013.7.1051 
[17] 
Alexander Zlotnik, Ilya Zlotnik. Finite element method with discrete transparent boundary conditions for the timedependent 1D Schrödinger equation. Kinetic and Related Models, 2012, 5 (3) : 639667. doi: 10.3934/krm.2012.5.639 
[18] 
Yue Feng, Yujie Liu, Ruishu Wang, Shangyou Zhang. A conforming discontinuous Galerkin finite element method on rectangular partitions. Electronic Research Archive, 2021, 29 (3) : 23752389. doi: 10.3934/era.2020120 
[19] 
Yuri Trakhinin. On wellposedness of the plasmavacuum interface problem: the case of nonelliptic interface symbol. Communications on Pure and Applied Analysis, 2016, 15 (4) : 13711399. doi: 10.3934/cpaa.2016.15.1371 
[20] 
Anya Désilles, Hélène Frankowska. Explicit construction of solutions to the Burgers equation with discontinuous initialboundary conditions. Networks and Heterogeneous Media, 2013, 8 (3) : 727744. doi: 10.3934/nhm.2013.8.727 
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