# Error analysis and uncertainty quantification for the heterogeneous transport equation in slab geometry

@article{Graham2019ErrorAA, title={Error analysis and uncertainty quantification for the heterogeneous transport equation in slab geometry}, author={Ivan G. Graham and M Parkinson and Robert Scheichl}, journal={IMA Journal of Numerical Analysis}, year={2019} }

We present an analysis of multilevel Monte Carlo (MLMC) techniques for the forward problem of uncertainty quantification for the radiative transport equation, when the coefficients (cross-sections) are heterogenous random fields. To do this we first give a new error analysis for the combined spatial and angular discretisation in the deterministic case, with error estimates that are explicit in the coefficients (and allow for very low regularity and jumps). This detailed error analysis is done…

## One Citation

### The Radiative Transport Equation with Heterogeneous Cross-Sections

- Mathematics2018 MATRIX Annals
- 2020

We consider the classical integral equation reformulation of the radiative transport equation (RTE) in a heterogeneous medium, assuming isotropic scattering. We prove an estimate for the norm of the…

## References

SHOWING 1-10 OF 46 REFERENCES

### The Radiative Transport Equation with Heterogeneous Cross-Sections

- Mathematics2018 MATRIX Annals
- 2020

We consider the classical integral equation reformulation of the radiative transport equation (RTE) in a heterogeneous medium, assuming isotropic scattering. We prove an estimate for the norm of the…

### Error Estimates for the Combined Spatial and Angular Approximations of the Transport Equation for Slab Geometry

- Mathematics
- 1983

We study the convergence of the discrete ordinates method in the numerical solution of the transport equation for slab geometry. In particular, the combined effect of spatial and angular…

### Finite Element Error Analysis of Elliptic PDEs with Random Coefficients and Its Application to Multilevel Monte Carlo Methods

- Mathematics, Computer ScienceSIAM J. Numer. Anal.
- 2013

A finite element approximation of elliptic partial differential equations with random coefficients is considered, which is used to perform a rigorous analysis of the multilevel Monte Carlo method for these elliptic problems that lack full regularity and uniform coercivity and boundedness.

### An adaptive nested source term iteration for radiative transfer equations

- Mathematics, Computer ScienceMath. Comput.
- 2020

A new approach to the numerical solution of radiative transfer equations with certified a posteriori error bounds is proposed, which allows for an iteration in a suitable, infinite dimensional function space that is guaranteed to converge with a fixed error reduction per step.

### Domain decomposition methods for nuclear reactor modelling with diffusion acceleration

- Mathematics
- 2016

In this thesis we study methods for solving the neutron transport equation (or linear Boltzmann equation). This is an integro-differential equation that describes the behaviour of neutrons during a…

### Uncertainty quantification for criticality problems using non-intrusive and adaptive Polynomial Chaos techniques

- Computer Science
- 2013

### On discontinuous Galerkin and discrete ordinates approximations for neutron transport equation and the critical eigenvalue

- Mathematics
- 2009

The objective of this paper is to give a mathematical framework for a fully discrete numerical approach for the study of the neutron transport equation in a cylindrical domain (container model). More…

### Numerical Analysis of a Non-Conforming Domain Decomposition for the Multigroup SPN Equations

- Mathematics
- 2018

In this thesis, we investigate the resolution of the SPN neutron transport equations in pressurized water nuclear reactor. These equations are a generalized eigenvalue problem. In our study, we first…

### Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients

- Mathematics, Computer ScienceNumerische Mathematik
- 2013

It is proved that convergence of the multilevel Monte Carlo algorithm for estimating any bounded, linear functional and any continuously Fréchet differentiable non-linear functional of the solution is convergence.