SIAM Journal on Numerical Analysis
The immersed interface method: a numerical approach for partial differential equations with interfaces
Channel flow of a viscous fluid in the boundary layer
Quarterly of Applied Mathematics
SIAM Journal on Numerical Analysis
Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients
SIAM Journal on Scientific Computing
Immersed Interface Methods for Neumann and Related Problems in Two and Three Dimensions
SIAM Journal on Scientific Computing
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
A Jump Condition Capturing Finite Difference Scheme for Elliptic Interface Problems
SIAM Journal on Scientific Computing
Journal of Computational Physics
A rothe-immersed interface method for a class of parabolic interface problems
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
A Coupling Interface Method for a Nonlinear Parabolic-Elliptic Problem
Numerical Analysis and Its Applications
Immersed Interface Difference Schemes for a Parabolic-Elliptic Interface Problem
Large-Scale Scientific Computing
A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations
Journal of Computational Physics
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
Journal of Computational and Applied Mathematics
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This paper develops the immersed interface method (IIM) due to [R.J. LeVeque, Z. Li, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal. 31 (1994) 1019-1044] for solving parabolic equations with singular own sources. New finite difference schemes are constructed to satisfy the discrete maximum principle. Convergence proof is provided. Numerical experiments show the efficiency of the proposed schemes.