A Space-Time Multiscale Method for Parabolic Problems
From MaRDI portal
Publication:5099849
DOI10.1137/21M1446605zbMath1493.65158arXiv2109.06647OpenAlexW3200042358MaRDI QIDQ5099849
Per Ljung, Roland Maier, Axel Målqvist
Publication date: 26 August 2022
Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2109.06647
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)
Related Items (7)
Neural Network Approximation of Coarse-Scale Surrogates in Numerical Homogenization ⋮ Multiscale methods for solving wave equations on spatial networks ⋮ Randomized Quasi-Optimal Local Approximation Spaces in Time ⋮ An adaptive global-local generalized FEM for multiscale advection-diffusion problems ⋮ Localized Orthogonal Decomposition for a Multiscale Parabolic Stochastic Partial Differential Equation ⋮ Fully discrete heterogeneous multiscale method for parabolic problems with multiple spatial and temporal scales ⋮ A transient global-local generalized FEM for parabolic and hyperbolic PDEs with multi-space/time scales
Cites Work
- Unnamed Item
- Unnamed Item
- Generalized multiscale finite element methods (GMsFEM)
- Space-time finite element methods for parabolic problems
- The heterogeneous multiscale methods
- The variational multiscale method -- a paradigm for computational mechanics
- On a BPX-preconditioner for P1 elements
- A multiscale finite element method for elliptic problems in composite materials and porous media
- Some observations on Babuška and Brezzi theories
- Multiscale techniques for parabolic equations
- The Schur complement and its applications
- Explicit computational wave propagation in micro-heterogeneous media
- Generalized multiscale finite element methods for space-time heterogeneous parabolic equations
- Relaxing the CFL condition for the wave equation on adaptive meshes
- Error-bounds for finite element method
- A space-time formulation for multiscale phenomena
- Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
- Nodal Interpolation Between First-Order Finite Element Spaces in 1D is Uniformly H 1-Stable
- Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization
- Localized orthogonal decomposition method for the wave equation with a continuum of scales
- Multigrid with Rough Coefficients and Multiresolution Operator Decomposition from Hierarchical Information Games
- Optimal Local Approximation Spaces for Generalized Finite Element Methods with Application to Multiscale Problems
- The heterogeneous multiscale method
- Localization of elliptic multiscale problems
- Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods
- Homogenization of Parabolic Equations with a Continuum of Space and Time Scales
- Generalized Inf-Sup Conditions for Chebyshev Spectral Approximation of the Stokes Problem
- Optimal $H^{p,{p/2}} $ Error Estimates for a Parabolic Galerkin Method
- Numerical Methods for Elliptic and Parabolic Partial Differential Equations
- Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
- A generalized finite element method for the strongly damped wave equation with rapidly varying data
- Computational Multiscale Methods for Linear Heterogeneous Poroelasticity
- Numerical Homogenization by Localized Orthogonal Decomposition
- A generalized finite element method for linear thermoelasticity
- Finite element quasi-interpolation and best approximation
- Oversampling for the Multiscale Finite Element Method
- An improved error bound for reduced basis approximation of linear parabolic problems
- Optimal Local Approximation Spaces for Parabolic Problems
- Fast mass lumped multiscale wave propagation modelling
- Numerical homogenization beyond scale separation
This page was built for publication: A Space-Time Multiscale Method for Parabolic Problems