| [1] Evans D J, Abdullah A R B. Group explicit methods for parabolic equations[J]. International Journal of Computer Mathematics, 1983, 14(1):73-105.[2] Dawson C N, Dupont T F. Explicit/Implicit, Conservative Domain Decomposition Procedures for Parabolic Problems Based on Block-Centered Finite Differences[J]. SIAM Journal on Numerical Analysis, 1994, 31(4):1045-1061.[3] Yuan G, Shen L. Stability and convergence of the explicit-implicit conservative domain decomposition procedure for parabolic problems[J]. Computers & Mathematics with Applications, 2004, 47(4):793-801.[4] Zhu S, Yuan G, Sun W. Convergence and stability of explicit/implicit schemes for parabolic equations with discontinuous coefficients[J]. International Journal of Numerical Analysis & Modeling, 2004, 1(2):131-146.[5] Dawson C N, Du Q, Dupont T F. A finite difference domain decomposition algorithm for numerical solution of the heat equation[J]. Mathematics of Computation, 1991, 57(195):63-71.[6] Sheng Z, Yuan G, Hang X. Unconditional stability of parallel difference schemes with second order accuracy for parabolic equation[J]. Applied Mathematics & Computation, 2007, 184(2):1015-1031.[7] Yuan G W, Hang X D, Sheng Z Q. Parallel difference schemes with interface extrapolation terms for quasi-linear parabolic systems[J]. Science in China, 2007, 50(2):253-275.[8] Zhu S. Conservative domain decomposition procedure with unconditional stability and secondorder accuracy[J]. Applied Mathematics & Computation, 2010, 216(11):3275-3282.[9] Yuan G, Yao Y, Yin L. A Conservative Domain Decomposition Procedure for Nonlinear Diffusion Problems on Arbitrary Quadrilateral Grids[J]. SIAM Journal on Scientific Computing, 2011, 33(3):1352-1368.[10] Hao W, Zhu S. Domain decomposition schemes with high-order accuracy and unconditional stability[J]. Applied Mathematics & Computation, 2013, 11(11):6170-6181.[11] Wang R, Zhang Y. Conservative domain decomposition procedure for the variable coefficient diffusion equation[J]. Journal of Information and Computing Science, 2014, 9(1):22-30.[12] Shi, Liao. Unconditional Stability of Corrected Explicit-Implicit Domain Decomposition Algorithms for Parallel Approximation of Heat Equations[J]. SIAM Journal on Numerical Analysis, 2006, 44(4):1584-1611.[13] Yuan G, Hang X. Conservative Parallel Schemes for Diffusion Equations[J]. Jisuan Wuli/chinese Journal of Computational Physics, 2010, 27(4):475-491.[14] Liang D, Du C. The efficient S-DDM scheme and its analysis for solving parabolic equations[J]. Journal of Computational Physics, 2014, 272(9):46-69.[15] Zhou Z, Liang D. The Mass-Preserving S-DDM Scheme for Two-Dimensional Parabolic Equations[J]. Communications in Computational Physics, 2016, 19(2):411-441.[16] Zhou Z, Liang D. The mass-preserving and modified-upwind splitting DDM scheme for time dependent convection diffusion equations[J]. Journal of Computational and Applied Mathematics, 2017, 317:247-273.[17] Droniou J. Finite volume schemes for diffusion equations:Introduction to and review of modern methods[J]. Mathematical Models & Methods in Applied Sciences, 2014, 24(8):1575-1619.[18] Sheng Z, Yuan G. The finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes[J]. Journal of Computational Physics, 2011, 230(7):2588-2604.[19] Lipnikov K, Shashkov M, Svyatskiy D, Vassilevski Y. Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes[J]. Journal of Computational Physics, 2007, 227(1):492-512.[20] Yuan G, Sheng Z. Monotone finite volume schemes for diffusion equations on polygonal meshes[J]. Journal of Computational Physics, 2008, 227(12):6288-6312.[21] Sheng Z, Yuan G. An improved monotone finite volume scheme for diffusion equation on polygonal meshes[J]. Journal of Computational Physics, 2012, 231(9):3739-3754.[22] Sheng Z, Yuan G. A Cell-Centered Nonlinear Finite Volume Scheme Preserving Fully Positivity for Diffusion Equation[J]. Journal of Scientific Computing, 2015, 1-25.[23] Sheng Z, Yue J, Yuan G. A parallel finite volume scheme preserving positivity for diffusion equation on distorted meshes[J]. Numerical Methods for Partial Differential Equations, 2017. |
