Stochastic variational multiscale analysis of the advection-diffusion equation: advective-diffusive regime and multi-dimensional problems
DOI10.1016/j.cma.2017.07.013zbMath1439.35587OpenAlexW2741959402MaRDI QIDQ2310045
Assad A. Oberai, Jason Li, Jayanth Jagalur-Mohan, Onkar Sahni
Publication date: 6 April 2020
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2017.07.013
uncertainty quantificationstochastic advection-diffusion equationprojection-based approximation for radical expressions of gPC expansions (e.g.square-root)stochastic stabilization parameterstochastic variational multiscale formulation
Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75) Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) PDEs with randomness, stochastic partial differential equations (35R60)
Cites Work
- A non-adapted sparse approximation of PDEs with stochastic inputs
- Solution verification, goal-oriented adaptive methods for stochastic advection-diffusion problems
- Variational multiscale stabilized FEM formulations for transport equations: Stochastic advection-diffusion and incompressible stochastic Navier-Stokes equations
- Sparse high order FEM for elliptic sPDEs
- A new finite element formulation for computational fluid dynamics. IX: Fourier analysis of space-time Galerkin/least-squares algorithms
- The variational multiscale method -- a paradigm for computational mechanics
- A stochastic projection method for fluid flow. II: Random process
- Iterative solution of systems of linear equations arising in the context of stochastic finite elements
- Stochastic Galerkin methods for the steady-state Navier-Stokes equations
- Non-intrusive low-rank separated approximation of high-dimensional stochastic models
- Modeling diffusion in random heterogeneous media: data-driven models, stochastic collocation and the variational multiscale method
- Variational multiscale a posteriori error estimation for multi-dimensional transport problems
- Variational Multiscale Analysis: The Fine-Scale Green's Function for Stochastic Partial Differential Equations
- Approximate optimal projection for reduced-order models
- Spectral Methods for Uncertainty Quantification
- A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
- The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
- Hierarchical Schur complement preconditioner for the stochastic Galerkin finite element methods
- Variational Multiscale Analysis: the Fine‐scale Green’s Function, Projection, Optimization, Localization, and Stabilized Methods
- High-Order Collocation Methods for Differential Equations with Random Inputs
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
