Results 41 to 50 of about 13,453,555 (238)

An exponential integration generalized multiscale finite element method for parabolic problems

Journal of Computational Physics, 2023
We consider linear and semilinear parabolic problems posed in high-contrast multiscale media in two dimensions. The presence of high-contrast multiscale media adversely affects the accuracy, stability, and overall efficiency of numerical approximations such as finite elements in space combined with some time integrator. In many cases, implementing time
Contreras, L.F., Pardo, D., Abreu, E., Muñoz-Matute, J., Diaz, C., Galvis, J.   +5 more
openaire   +3 more sources

Sparse Generalized Multiscale Finite Element Methods and their applications [PDF]

International Journal for Multiscale Computational Engineering, 2015
In a number of previous papers, local (coarse grid) multiscale model reduction techniques are developed using a Generalized Multiscale Finite Element Method. In these approaches, multiscale basis functions are constructed using local snapshot spaces, where a snapshot space is a large space that represents the solution behavior in a coarse block.
Chung, Eric T., Efendiev, Yalchin, Li, Guanglian, Leung, Wing Tat   +3 more
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On the adaptive selection of the parameter in stabilized finite element approximations [PDF]

, 2013
A systematic approach is developed for the selection of the stabilization parameter for stabilized finite element approximation of the Stokes problem, whereby the parameter is chosen to minimize a computable upper bound for the error in the approximation.
Rankin, Richard Andrew Robert, Barrenechea, Gabriel, Ainsworth, Mark, Allendes Flores, Alejandro Ignacio   +3 more
core   +4 more sources

A weak Galerkin generalized multiscale finite element method

Journal of Computational and Applied Mathematics, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lin Mu 0002, Junping Wang, Xiu Ye
openaire   +3 more sources

A generalized multiscale finite element method for poroelasticity problems II: Nonlinear coupling [PDF]

Journal of Computational and Applied Mathematics, 2016
arXiv admin note: text overlap with arXiv:1304.5188 by other ...
Donald L. Brown, Maria V. Vasilyeva
openaire   +5 more sources

Generalized Multiscale Finite Element Methods with energy minimizing oversampling

International Journal for Numerical Methods in Engineering, 2018
SummaryIn this paper, we propose a general concept for constructing multiscale basis functions within Generalized Multiscale Finite Element Method, which uses oversampling and stable decomposition. The oversampling refers to using larger regions in constructing multiscale basis functions and stable decomposition allows estimating the local errors.
Eric Chung, Yalchin Efendiev, Wing Tat Leung   +2 more
openaire   +2 more sources

A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations [PDF]

, 2013
An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steadystate and the transient setting.
Volker, John, Barrenechea, Gabriel, Knobloch, Petr   +2 more
core   +2 more sources

Multiscale Simulation of 2D Heat Transfer in Composite Media Based on Global–Local Enrichment Functions

Mathematics
In this study, the extended finite element method (XFEM) was integrated into the generalized multiscale finite element method with global–local enrichment (GFEMgl) to simulate 2D heat conduction in highly heterogeneous materials (i.e., matrixes with ...
Guangzhong Liu, Jiamin Guo, Yan Bao, Huan Ping   +3 more
doaj   +1 more source

Generalized multiscale finite element methods for problems in perforated heterogeneous domains [PDF]

Applicable Analysis, 2015
Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales (see Figure 1 for the illustration of a perforated domain). Moreover, these problems are intrinsically multiscale and their discretizations can yield very large linear or ...
Chung, Eric T., Efendiev, Yalchin, Li, Guanglian, Vasilyeva, Maria   +3 more
openaire   +4 more sources

Generalized Multiscale Finite Element Method for the Steady State Linear Boltzmann Equation [PDF]

Multiscale Modeling & Simulation, 2020
The Boltzmann equation, as a model equation in statistical mechanics, is used to describe the statistical behavior of a large number of particles driven by the same physics laws. Depending on the media and the particles to be modeled, the equation has slightly different forms.
Eric T. Chung 0001, Yalchin Efendiev, Yanbo Li, Qin Li 0007   +3 more
openaire   +2 more sources