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Multiscale methods for advection-diffusion problems
1. | Mathematica Department, University of Basel, Rheinsprung 21, CH-4051 Switzerland |
[1] |
Alexander Mielke. Weak-convergence methods for Hamiltonian multiscale problems. Discrete and Continuous Dynamical Systems, 2008, 20 (1) : 53-79. doi: 10.3934/dcds.2008.20.53 |
[2] |
Patrick Henning, Mario Ohlberger. The heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift. Networks and Heterogeneous Media, 2010, 5 (4) : 711-744. doi: 10.3934/nhm.2010.5.711 |
[3] |
Patrick Henning, Mario Ohlberger. A-posteriori error estimate for a heterogeneous multiscale approximation of advection-diffusion problems with large expected drift. Discrete and Continuous Dynamical Systems - S, 2016, 9 (5) : 1393-1420. doi: 10.3934/dcdss.2016056 |
[4] |
Assyr Abdulle, Yun Bai, Gilles Vilmart. Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Discrete and Continuous Dynamical Systems - S, 2015, 8 (1) : 91-118. doi: 10.3934/dcdss.2015.8.91 |
[5] |
Patrick Henning, Mario Ohlberger. Error control and adaptivity for heterogeneous multiscale approximations of nonlinear monotone problems. Discrete and Continuous Dynamical Systems - S, 2015, 8 (1) : 119-150. doi: 10.3934/dcdss.2015.8.119 |
[6] |
Fabio Camilli, Claudio Marchi. On the convergence rate in multiscale homogenization of fully nonlinear elliptic problems. Networks and Heterogeneous Media, 2011, 6 (1) : 61-75. doi: 10.3934/nhm.2011.6.61 |
[7] |
Lijian Jiang, Yalchin Efendiev, Victor Ginting. Multiscale methods for parabolic equations with continuum spatial scales. Discrete and Continuous Dynamical Systems - B, 2007, 8 (4) : 833-859. doi: 10.3934/dcdsb.2007.8.833 |
[8] |
Dag Lukkassen, Annette Meidell, Peter Wall. Multiscale homogenization of monotone operators. Discrete and Continuous Dynamical Systems, 2008, 22 (3) : 711-727. doi: 10.3934/dcds.2008.22.711 |
[9] |
Yoonsang Lee, Bjorn Engquist. Variable step size multiscale methods for stiff and highly oscillatory dynamical systems. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 1079-1097. doi: 10.3934/dcds.2014.34.1079 |
[10] |
Nils Svanstedt. Multiscale stochastic homogenization of monotone operators. Networks and Heterogeneous Media, 2007, 2 (1) : 181-192. doi: 10.3934/nhm.2007.2.181 |
[11] |
Michael Herty, Giuseppe Visconti. Kinetic methods for inverse problems. Kinetic and Related Models, 2019, 12 (5) : 1109-1130. doi: 10.3934/krm.2019042 |
[12] |
Olivier Pironneau, Alexei Lozinski, Alain Perronnet, Frédéric Hecht. Numerical zoom for multiscale problems with an application to flows through porous media. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 265-280. doi: 10.3934/dcds.2009.23.265 |
[13] |
Donald L. Brown, Vasilena Taralova. A multiscale finite element method for Neumann problems in porous microstructures. Discrete and Continuous Dynamical Systems - S, 2016, 9 (5) : 1299-1326. doi: 10.3934/dcdss.2016052 |
[14] |
Zhan Chen, Yuting Zou. A multiscale model for heterogeneous tumor spheroid in vitro. Mathematical Biosciences & Engineering, 2018, 15 (2) : 361-392. doi: 10.3934/mbe.2018016 |
[15] |
Frederike Kissling, Christian Rohde. The computation of nonclassical shock waves with a heterogeneous multiscale method. Networks and Heterogeneous Media, 2010, 5 (3) : 661-674. doi: 10.3934/nhm.2010.5.661 |
[16] |
Juan Wen, Yaling He, Yinnian He, Kun Wang. Stabilized finite element methods based on multiscale enrichment for Allen-Cahn and Cahn-Hilliard equations. Communications on Pure and Applied Analysis, 2022, 21 (6) : 1873-1894. doi: 10.3934/cpaa.2021074 |
[17] |
Jana Kopfová. Nonlinear semigroup methods in problems with hysteresis. Conference Publications, 2007, 2007 (Special) : 580-589. doi: 10.3934/proc.2007.2007.580 |
[18] |
Jie Sun. On methods for solving nonlinear semidefinite optimization problems. Numerical Algebra, Control and Optimization, 2011, 1 (1) : 1-14. doi: 10.3934/naco.2011.1.1 |
[19] |
José A. Cañizo, Alexis Molino. Improved energy methods for nonlocal diffusion problems. Discrete and Continuous Dynamical Systems, 2018, 38 (3) : 1405-1425. doi: 10.3934/dcds.2018057 |
[20] |
Dang Van Hieu. Projection methods for solving split equilibrium problems. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2331-2349. doi: 10.3934/jimo.2019056 |
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