P1$$ {P}_1 $$‐nonconforming quadrilateral finite element space with periodic boundary conditions: Part II. Application to the nonconforming heterogeneous multiscale method
DOI10.1002/num.23009arXiv2201.10661MaRDI QIDQ6088147
Imbo Sim, Jaeryun Yim, Dongwoo Sheen
Publication date: 13 December 2023
Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2201.10661
Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Iterative numerical methods for linear systems (65F10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Direct numerical methods for linear systems and matrix inversion (65F05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Numerical integration (65D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Generalized multiscale finite element methods (GMsFEM)
- A multi-scale finite element method for the Stokes problem
- Convergence and optimality of the adaptive Morley element method
- A short and versatile finite element multiscale code for homogenization problems
- Adaptive finite element heterogeneous multiscale method for homogenization problems
- Nonconforming generalized multiscale finite element methods
- The heterogeneous multiscale methods
- A new a posteriori error estimate for the Morley element
- Non-homogeneous media and vibration theory
- Efficient solvers for incompressible flow problems. An algorithmic and computational approach
- The variational multiscale method -- a paradigm for computational mechanics
- A multiscale finite element method for elliptic problems in composite materials and porous media
- A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems
- Nonconforming quadrilateral finite elements: a correction
- A locking-free nonconforming finite element method for planar linear elasticity
- Multi-scale finite-volume method for elliptic problems in subsurface flow simulation.
- MsFEM à la Crouzeix-Raviart for highly oscillatory elliptic problems
- A quadrilateral Morley element for biharmonic equations
- A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier-Stokes equations
- Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems
- A quadrilateral nonconforming finite element for linear elasticity problem
- Analysis of the heterogeneous multiscale method for elliptic homogenization problems
- The heterogeneous multiscale method
- Nonconforming Multiscale Finite Element Method for Stokes Flows in Heterogeneous Media. Part I: Methodologies and Numerical Experiments
- Multiscale Finite Element Methods
- Morley type non-C 0 nonconforming rectangular plate finite elements on anisotropic meshes
- Asymptotic and numerical homogenization
- Simple nonconforming quadrilateral Stokes element
- Linear Finite Element Methods for Planar Linear Elasticity
- Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
- Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
- Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients
- P1-Nonconforming Quadrilateral Finite Element Methods for Second-Order Elliptic Problems
- Numerical Homogenization of Nonlinear Random Parabolic Operators
- Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
- Convergence of a Nonconforming Multiscale Finite Element Method
- An MsFEM Type Approach for Perforated Domains
- Crouzeix-Raviart MsFEM with Bubble Functions for Diffusion and Advection-Diffusion in Perforated Media
- Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales
- Finite Elements
- Stable cheapest nonconforming finite elements for the Stokes equations
