Parameter Identification in Uncertain Scalar Conservation Laws Discretized with the Discontinuous Stochastic Galerkin Scheme
DOI10.4208/cicp.OA-2019-0221MaRDI QIDQ5162353
Claudia Totzeck, Louisa Schlachter
Publication date: 2 November 2021
Published in: Communications in Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1912.09813
optimizationparameter identificationdiscontinuous Galerkinuncertainty quantificationpolynomial chaosstochastic Galerkinmultielement
Optimality conditions for problems involving partial differential equations (49K20) First-order nonlinear hyperbolic equations (35L60) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems (37L65) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Numerical analysis (65-XX) PDEs in connection with statistics (35Q62)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Adjoint IMEX-based schemes for control problems governed by hyperbolic conservation laws
- On high order strong stability preserving Runge-Kutta and multi step time discretizations
- Long-term behavior of polynomial chaos in stochastic flow simulations
- Uncertainty quantification for systems of conservation laws
- TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
- Shift-differentiability of the flow generated by a conservation law
- Runge-Kutta methods in optimal control and the transformed adjoint system
- On the consistency of Runge-Kutta methods up to order three applied to the optimal control of scalar conservation laws
- Uncertainty quantification in control problems for flocking models
- A third order hierarchical basis WENO interpolation for sparse grids with application to conservation laws with uncertain data
- Uncertainty analysis for the steady-state flows in a dual throat nozzle
- A hyperbolicity-preserving stochastic Galerkin approximation for uncertain hyperbolic systems of equations
- Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems
- Filtered stochastic Galerkin methods for hyperbolic equations
- Instantaneous control of interacting particle systems in the mean-field limit
- Monte Carlo gPC methods for diffusive kinetic flocking models with uncertainties
- A hyperbolicity-preserving discontinuous stochastic Galerkin scheme for uncertain hyperbolic systems of equations
- Polynomial chaos methods for hyperbolic partial differential equations. Numerical techniques for fluid dynamics problems in the presence of uncertainties
- An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
- Adjoint-based derivative computations for the optimal control of discontinuous solutions of hyperbolic conservation laws
- Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data
- Non-intrusive Uncertainty Propagation with Error Bounds for Conservation Laws Containing Discontinuities
- Inverse problems: A Bayesian perspective
- Discretization of Optimal Control Problems
- Uncertainty Quantification for Hyperbolic Systems of Conservation Laws
- On the treatment of distributed uncertainties in PDE-constrained optimization
- The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
- Multilevel Monte Carlo Path Simulation
- Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
- Optimization with PDE Constraints
- Spectral Methods for Uncertainty Quantification
- TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
- A Class of Bases in $L^2$ for the Sparse Representation of Integral Operators
- Discrete Adjoint Approximations with Shocks
- The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
- The relaxation schemes for systems of conservation laws in arbitrary space dimensions
- Numerical Methods for the Optimal Control of Scalar Conservation Laws
- Total variation diminishing schemes in optimal control of scalar conservation laws
- Particle Based gPC Methods for Mean-Field Models of Swarming with Uncertainty
- Bayesian Model Calibration with Interpolating Polynomials based on Adaptively Weighted Leja Nodes
- Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations
- Analysis of the Ensemble Kalman Filter for Inverse Problems
- FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
- Numerical Solution of Scalar Conservation Laws with Random Flux Functions
- The Homogeneous Chaos
- Mean-Field Optimal Control and Optimality Conditions in the Space of Probability Measures
- Numerical optimization. Theoretical and practical aspects. Transl. from the French
This page was built for publication: Parameter Identification in Uncertain Scalar Conservation Laws Discretized with the Discontinuous Stochastic Galerkin Scheme
