Multiscale finite-element methods (MFEM)
Generalized multiscale finite element methods (GMsFEM)
... reduced-order methods fail to give a small dimensional output solution space when the physical solution has multiscale ...reduced-order methods is that the reduced solution space needs to be ...
29
Generalization of Mixed Multiscale Finite Element Methods with Applications
... mixed methods for the Hellinger Reissner formulation [39, ...generalized multiscale finite element method, we build a conform- ing multiscale coarse space with strong-symmetry ...
165
Mixed multiscale finite element methods for stochastic porous media flows
... pre-computed multiscale basis functions can be repeatedly used for different boundary conditions/source terms and for dynamic two-phase flow and transport ...classical multiscale finite ...
24
Adaptivity and Online Basis Construction for Generalized Multiscale Finite Element Methods
... GENERALIZED MULTISCALE FINITE ELEMENT METHODS FOR WAVE PROPAGATION IN HETEROGENEOUS MEDIA ...include finite difference methods, finite ele- ment methods, and ...
165
Stabilized finite element methods based on multiscale enrichment for the Stokes problem
... STABILIZED FINITE ELEMENT METHODS BASED ON MULTISCALE ENRICHMENT FOR THE STOKES PROBLEM ∗ RODOLFO ARAYA † , GABRIEL ...finite element methods for the Stokes problem considering ...
27
Heterogeneous multiscale finite element methods for advection-diffusion and nonlinear elliptic multiscale problems
... heterogeneous multiscale finite element method for mono- tone elliptic operators with rapid ...elliptic multiscale problem with -periodic ...
160
Some Applications of the Generalized Multiscale Finite Element Method
... GENERALIZED MULTISCALE FINITE ELEMENT METHODS FOR SECOND-ORDER LINEAR ELASTICITY EQUATIONS ? ...Galerkin methods allow avoid- ing penalty parameters though they involve partition of ...
126
The variational multiscale method for mixed finite element formulations
... instead. Finite element methods based on mixed formulations (or “reduced order forms”) of the PDE were first proposed in the 60s ...the finite element ...
97
A multiscale finite element technique for nonlinear multi-phase materials
... bounding methods (see [5, 6]). The variational bounding methods are based on suitable variational (minimum energy) principles and provide upper and lower bounds for the overall properties of the ...
38
Finite element heterogeneous multiscale method for Elastic Waves in Heterogeneous Media
... Alternatively, multiscale FE or FD methods determine during pre-processing new mul- tiscale FE or FD basis functions by numerically solving appropriate local ...and multiscale basis functions are ...
34
An adaptive finite element heterogeneous multiscale method for Stokes flow in porous media
... |e mic | H 1 (Ω) cη mic,Ω Figure 25: Medium C: DS-FE-HMM error analysis (macro: P 1 , micro: P 2 / P 1 , periodic BC). and its computational cost is independent of the pore size. We have focused on a class of problems ...
30
Finite Element Heterogeneous Multiscale Method for the Wave Equation: Long Time Effects
... For the spatial discretization, we use standard FEMs for the macro- and the microsolver. The resulting second-order system of ordinary differential equations is integrated in time with the second-order leapfrog scheme. ...
28
Analysis of the finite element heterogeneous multiscale method for nonmonotone elliptic homogenization problems
... the multiscale nature of the medium, described in (1) through a nonlinear multi- scale conductivity tensor a ε (x, u ε (x)), is not taken into account in the modeling due to the high computational cost in solving ...
22
Consistent local projection stabilized finite element methods
... stabilized methods where stabilized parameters are defined once and for all with respect to the integral of enriching basis ...stabilized finite element method (see ...Variational Multiscale ...
28
Stabilized finite element methods for the generalized Oseen problem
... finite element schemes on isotropic ...These methods are closely related to the concept of variational multiscale methods which seems to provide a new approach to large eddy ...
14
A Large Strains Finite Element Multiscale Approach
... For Peer Review Only 11. Conclusions A novel formulation for multiscale finite element analysis of materials with microvoids undergoing large strains is proposed in this paper. The technique proved ...
24
Finite Element Analysis of Multiscale Composite Beams
... layered multiscale composite beam ...The finite element analysis is a process in which the particular component is converted into small elements called discretization process, the elements are ...
8
INTRODUCTION to FINITE ELEMENT METHODS
... Deleted Topics. All advanced analysis material dealing with variational calculus and direct approx- imation methods such as Rayleigh-Ritz, Galerkin, least squares and collocation, was eliminated by 1990. The few ...
11
Finite element methods for surface PDEs
... finite element method In some applications it may be convenient to avoid triangulating a ...finite element spaces are ...finite element space and an appropriate discretization of the surface partial ...
110
Finite Element Methods Lecture Notes
... Combined Hybrid Using the foregoing classification, we can state the topic of this book more precisely: the computational analysis of linear static structural problems by the Finite Elem[r] ...
1177