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Article Contents

# An attempt at classifying homogenization-based numerical methods

• In this note, a classification of Homogenization-Based Numerical Methods and (in particular) of Numerical Methods that are based on the Two-Scale Convergence is done. In this classification stand: Direct Homogenization-Based Numerical Methods; H-Measure-Based Numerical Methods; Two-Scale Numerical Methods and TSAPS: Two-Scale Asymptotic Preserving Schemes.
Mathematics Subject Classification: Primary: 65L99, 65M99, 65N99.

 Citation:

•  [1] A. Abdulle, Y. Bai and G. Vilmart, Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems, Discrete and Continuous Dynamical Systems - Serie S. Special Issue on Numerical Methods based on Homogenization and Two-Scale Convergence, In press. [2] A. Back and E. Frénod, Geometric two-scale convergence on manifold and applications to the Vlasov equation, Discrete and Continuous Dynamical Systems - Serie S. Special Issue on Numerical Methods based on Homogenization and Two-Scale Convergence, In press. [3] J.-P. Bernard, E. Frénod and A. Rousseau, Paralic confinement computations in coastal environment with interlocked areas, Discrete and Continuous Dynamical Systems - Serie S. Special Issue on Numerical Methods based on Homogenization and Two-Scale Convergence, In press. [4] N. Crouseilles, E. Frenod, S. Hirstoaga and A. Mouton, Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field, Mathematical Models and Methods in Applied Sciences, 23 (2013), 1527-1559.doi: 10.1142/S0218202513500152. [5] I. Faye, E. Frénod and D. Seck, Two-scale numerical simulation of sand transport problems, Discrete and Continuous Dynamical Systems - Serie S. Special Issue on Numerical Methods based on Homogenization and Two-Scale Convergence, In press. [6] E. Frénod, S. Histoaga and E. Sonnendrücker, An exponential integrator for a highly oscillatory Vlasov equation, Discrete and Continuous Dynamical Systems - Serie S. Special Issue on Numerical Methods based on Homogenization and Two-Scale Convergence, In press. [7] P. Henning and M. Ohlberger, Error control and adaptivity for heterogeneous multiscale approximations of nonlinear monotone problems, Discrete and Continuous Dynamical Systems - Serie S. Special Issue on Numerical Methods based on Homogenization and Two-Scale Convergence, In press. [8] S. Jin, Efficient asymptotic-preserving (ap) schemes for some multiscale kinetic equations, SIAM Journal of Scientific Computing, 21 (1999), 441-454.doi: 10.1137/S1064827598334599. [9] V. Laptev, Deterministic homogenization for media with barriers, Discrete and Continuous Dynamical Systems - Serie S. Special Issue on Numerical Methods based on Homogenization and Two-Scale Convergence, In press. [10] F. Legoll and W. Minvielle, Variance reduction using antithetic variables for a nonlinear convex stochastic homogenization problem, Discrete and Continuous Dynamical Systems - Serie S. Special Issue on Numerical Methods based on Homogenization and Two-Scale Convergence, In press. [11] M. Lutz, Application of Lie transform techniques for simulation of a charged particle beam, Discrete and Continuous Dynamical Systems - Serie S. Special Issue on Numerical Methods based on Homogenization and Two-Scale Convergence, In press. [12] Tartar, Multi-scales h-measures, Discrete and Continuous Dynamical Systems - Serie S. Special Issue on Numerical Methods based on Homogenization and Two-Scale Convergence, In press. [13] X. Xu and S. Yue, Homogenization of thermal-hydro-mass transfer processes, Discrete and Continuous Dynamical Systems - Serie S. Special Issue on Numerical Methods based on Homogenization and Two-Scale Convergence, In press.
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