Cross-mode stabilized stochastic shallow water systems using stochastic finite element methods

DOI10.1016/j.cma.2022.115873OpenAlexW4317039054MaRDI QIDQ2683460

Chen Chen, Eirik Valseth, Clint N. Dawson

Publication date: 10 February 2023

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.11396

zbMATH Keywords

shallow water equationsuncertainty quantificationstochastic Galerkincross-mode stabilizationincremental pressure correction

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) PDEs with randomness, stochastic partial differential equations (35R60)

Uses Software

• FIAT
• DOLFIN
• FEniCS
• SyFi
• ADCIRC
• UFL

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some models for rainfall based on stochastic point processes
• Automated solution of differential equations by the finite element method. The FEniCS book
• A non-intrusive method for the calculation of strict and efficient bounds of calculated outputs of interest in linear viscoelasticity problems
• A new finite element formulation for computational fluid dynamics. II. Beyond SUPG
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows
• Unconditional stability and long-term behavior of transient algorithms for the incompressible Navier-Stokes and Euler equations
• A hyperbolicity-preserving stochastic Galerkin approximation for uncertain hyperbolic systems of equations
• Hyperbolicity-preserving and well-balanced stochastic Galerkin method for two-dimensional shallow water equations
• A polynomial chaos framework for probabilistic predictions of storm surge events
• Hyperbolic stochastic Galerkin formulation for the \(p\)-system
• Least squares polynomial chaos expansion: a review of sampling strategies
• Formulation and application of the adaptive hydraulics three-dimensional shallow water and transport models
• Hp discontinuous Galerkin methods for advection dominated problems in shallow water flow
• Continuous interior penalty finite element method for the time-dependent Navier-Stokes equations: space discretization and convergence
• Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs
• Robust Uncertainty Propagation in Systems of Conservation Laws with the Entropy Closure Method
• DOLFIN
• Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
• Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
• Computation of moving boundaries and interfaces and stabilization parameters
• Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations
• Algorithm 839
• Unified form language
• The Monte Carlo Method
• Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations

This page was built for publication: Cross-mode stabilized stochastic shallow water systems using stochastic finite element methods