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### Citations

544 |
Streamline Upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations,
- Brooks, Hughes
- 1982
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Citation Context ... that turns out to be unreliable (see for instance the example considered in Section 4.1, with numerical results depicted in Fig. 2). The same bad behavior holds for finite difference schemes as well =-=[6]-=-. This is not a problem of how one obtains the discretization (finite element or difference), but of0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −30 −20 −10 0 x M em Fig. 2. Steady state solutions for smal... |

207 |
The Book of GENESIS: Exploring Realistic Neural Models With the GEneral NEural SImulation System. Telos,
- Bower, Beeman
- 1998
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Citation Context ...erogeneities approach infinity. That is not the whole story, since the heterogeneity must have some sort of ‘‘pattern’’, being periodic or random for instance. Such assumptions are often questionable =-=[3,37]-=-. Motivated by such concerns, we investigate the cable equationmake neuroscience so challenging putational point of view are the m scales present in most neurologica what is steadily being considere a... |

47 | Traveling fronts and wave propagation failure in an inhomogeneous neural network
- Bressloff
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Citation Context .... E-mail addresses: alm@lncc.br (A.L. Madureira), daniele@lncc.br (D.Q.M. Madureira), pedro.oliveira-pinheiro@insa-lyon.frcommonly employed, along with various degrees of neurological based arguments =-=[4,5,7,17,34,36,39,37,44,46]-=-. cm @V̂ s ‘d @2V̂ 2 þsmV̂ þ ŝinðV̂V inÞþ ŝexðV̂VexÞ 0[2,3,8,22,27–30,40–42,45,49]. Powerful mathematical tools from asymptotic analysis, like homogenization, matching asymptotics, singular per... |

47 |
An introduction to homogenization. Oxford
- Cioranescu, Donato
- 1999
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Citation Context ...ribution of synapses. In a recent important paper, Meunier and d’Incamps modeled by variants of cable equations, and inquired when the process of mathematical homogenization was valid. Homogenization =-=[9]-=- is a mathematical technique that, given a detailed model describing all the physical properties of the dendrites, ‘‘replaces’’ it by a homogeneous, simpler to solve, equation. It is like replacing a ... |

45 | The NEURON - Carnevale, Hines - 2006 |

11 | Kinetic theory for neuronal network dynamics.
- Cai, Tao, et al.
- 2006
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Citation Context .... E-mail addresses: alm@lncc.br (A.L. Madureira), daniele@lncc.br (D.Q.M. Madureira), pedro.oliveira-pinheiro@insa-lyon.frcommonly employed, along with various degrees of neurological based arguments =-=[4,5,7,17,34,36,39,37,44,46]-=-. cm @V̂ s ‘d @2V̂ 2 þsmV̂ þ ŝinðV̂V inÞþ ŝexðV̂VexÞ 0[2,3,8,22,27–30,40–42,45,49]. Powerful mathematical tools from asymptotic analysis, like homogenization, matching asymptotics, singular per... |

10 | Diusion of Protein Receptors on a Cylindrical Dendritic Membrane with Partially Absorbing Traps
- Bresslo, Earnshaw, et al.
(Show Context)
Citation Context .... E-mail addresses: alm@lncc.br (A.L. Madureira), daniele@lncc.br (D.Q.M. Madureira), pedro.oliveira-pinheiro@insa-lyon.frcommonly employed, along with various degrees of neurological based arguments =-=[4,5,7,17,34,36,39,37,44,46]-=-. cm @V̂ s ‘d @2V̂ 2 þsmV̂ þ ŝinðV̂V inÞþ ŝexðV̂VexÞ 0[2,3,8,22,27–30,40–42,45,49]. Powerful mathematical tools from asymptotic analysis, like homogenization, matching asymptotics, singular per... |

10 |
T h e o r e t i c a l N e u r o s c i e n c e : Computational and Mathematical Modeling of Neural Systems
- Dayan, Abbott
- 2001
(Show Context)
Citation Context ...llent accuracy, and that allows for great efficiency when several branches are coupled. We next consider a transient problem, with the parameters being the same as in Section 4.1 and tm 102 s, see =-=[10]-=-. After discretizing in space and obtaining a system of ordinary equations, we use backward Euler’s method for time discretization, yielding an implicit scheme. In all tests we consider the time step ... |

2 | Bubble stabilization of discontinuous Galerkin methods,
- Antonietti, Brezzi, et al.
- 2009
(Show Context)
Citation Context ...ations, finite elements and finite differences yield comparable results. However, when standard schemes do not work well, modern variants of finite elements come as an viable option of discretization =-=[1,12,13,18,19,26]-=-. One variant is the multiscale finite element method (MsFEM) [13–16,31,32,35], which we explore here. The idea behind multiscale methods to solve heterogeneous systems is that one has to first solve ... |

2 | Numerical solution of calcium-mediated dendritic branch model - Baer, Crook, et al. |