Optimal Local Approximation Spaces for Parabolic Problems
DOI10.1137/20M1384294zbMath1487.65157arXiv2012.02759OpenAlexW4220736807MaRDI QIDQ5865254
Julia Schleuß, Kathrin Smetana
Publication date: 13 June 2022
Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2012.02759
generalized finite element methodparabolic problemsa priori error boundmultiscale methodsKolmogorov \(n\)-widthspace-time Petrov-Galerkin methods
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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)
Related Items
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- Local boundedness property for parabolic BVP's and the Gaussian upper bound for their Green functions
- Generalized multiscale finite element methods (GMsFEM)
- A class of discontinuous Petrov-Galerkin methods. I: The transport equation
- Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients
- A reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks
- Model order reduction in porous media flow simulation using quadratic bilinear formulation
- The heterogeneous multiscale methods
- A space-time DPG method for the heat equation
- Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system
- On the Hölder continuity of bounded weak solutions of quasilinear parabolic systems
- Compact sets in the space \(L^ p(0,T;B)\)
- The variational multiscale method -- a paradigm for computational mechanics
- A multiscale finite element method for elliptic problems in composite materials and porous media
- The partition of unity finite element method: basic theory and applications
- Multiscale coarse spaces for overlapping Schwarz methods based on the ACMS space in 2D
- Multiscale techniques for parabolic equations
- Global estimates for nonlinear parabolic equations
- Generalized multiscale finite element methods for space-time heterogeneous parabolic equations
- Multiscale-spectral GFEM and optimal oversampling
- Boundary estimates for solutions to linear degenerate parabolic equations
- Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps
- A space-time formulation for multiscale phenomena
- Optimal Local Approximation Spaces for Component-Based Static Condensation Procedures
- A Static condensation Reduced Basis Element method : approximation anda posteriorierror estimation
- A literature survey of low-rank tensor approximation techniques
- Machine Computation Using the Exponentially Convergent Multiscale Spectral Generalized Finite Element Method
- Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization
- Localized Bases for Finite-Dimensional Homogenization Approximations with Nonseparated Scales and High Contrast
- The AL Basis for the Solution of Elliptic Problems in Heterogeneous Media
- Port reduction in parametrized component static condensation: approximation and a posteriori error estimation
- The localized reduced basis multiscale method for two-phase flows in porous media
- 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
- Space-time adaptive wavelet methods for parabolic evolution problems
- A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions
- Randomized Local Model Order Reduction
- Localization of elliptic multiscale problems
- Analysis of the heterogeneous multiscale method for parabolic homogenization problems
- Gaussian estimates for fundamental solutions of second order parabolic systems with time-independent coefficients
- Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients
- ARPACK Users' Guide
- A Particle-Partition of Unity Method for the Solution of Elliptic, Parabolic, and Hyperbolic PDEs
- Dual-Primal FETI Methods for Three-Dimensional Elliptic Problems with Heterogeneous Coefficients
- (Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov--Galerkin Methods
- A Localization Strategy for Data Assimilation; Application to State Estimation and Parameter Estimation
- The Reduced Basis Element Method: Application to a Thermal Fin Problem
- An Introduction to Partial Differential Equations
- Adaptive Petrov--Galerkin Methods for First Order Transport Equations
- Stability of sparse space-time finite element discretizations of linear parabolic evolution equations
- Can a finite element method perform arbitrarily badly?
- Stability of Galerkin discretizations of a mixed space–time variational formulation of parabolic evolution equations
- Static Condensation Optimal Port/Interface Reduction and Error Estimation for Structural Health Monitoring
- 6 Localized model reduction for parameterized problems
- Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions
- Randomized Sampling for Basis Function Construction in Generalized Finite Element Methods
- Towards Automatic and Reliable Localized Model Order Reduction
- An improved error bound for reduced basis approximation of linear parabolic problems
- Optimized Schwarz Methods
- A reduced-basis element method
- Data‐driven physics‐based digital twins via a library of component‐based reduced‐order models