paper.bib

@inproceedings{smolyak1963quadrature,
  title={Quadrature and interpolation formulas for tensor products of certain classes of functions},
  author={Smolyak, Sergei Abramovich},
  booktitle={Doklady Akademii Nauk},
  volume={148},
  number={5},
  pages={1042--1045},
  year={1963},
  organization={Russian Academy of Sciences}
}

@article{babuvska2007stochastic,
  title={A stochastic collocation method for elliptic partial differential equations with random input data},
  author={Babu{\v{s}}ka, Ivo and Nobile, Fabio and Tempone, Ra{\'u}l},
  journal={SIAM Journal on Numerical Analysis},
  volume={45},
  number={3},
  pages={1005--1034},
  year={2007},
  publisher={SIAM},
  doi = {10.1137/100786356}
}


@article{nobile2008sparse,
  title={A sparse grid stochastic collocation method for partial differential equations with random input data},
  author={Nobile, Fabio and Tempone, Ra{\'u}l and Webster, Clayton G},
  journal={SIAM Journal on Numerical Analysis},
  volume={46},
  number={5},
  pages={2309--2345},
  year={2008},
  publisher={SIAM},
  doi = {10.1137/060663660}
}

@article{ma2009adaptive,
  title={An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations},
  author={Ma, Xiang and Zabaras, Nicholas},
  journal={Journal of Computational Physics},
  volume={228},
  number={8},
  pages={3084--3113},
  year={2009},
  publisher={Elsevier},
  doi = {10.1016/j.jcp.2009.01.006}
}

@article{gates2015multilevel,
  title={A multilevel adaptive sparse grid stochastic collocation approach to the non-smooth forward propagation of uncertainty in discretized problems},
  author={Gates, Robert L and Bittens, Maximilian R},
  journal={arXiv preprint arXiv:1509.01462},
  year={2015},
  doi = {10.48550/arXiv.1509.01462}
}

@article{bittens2022vtufilehandler,
  title={VTUFileHandler: A VTU library in the {J}ulia language that implements an algebra for basic mathematical operations on VTU data},
  author={Bittens, Maximilian},
  journal={Journal of Open Source Software},
  volume={7},
  number={73},
  pages={4300},
  year={2022},
  doi = {10.21105/joss.04300}
}

@article{schroeder2000visualizing,
  title={Visualizing with VTK: a tutorial},
  author={Schroeder, William J and Avila, Lisa Sobierajski and Hoffman, William},
  journal={IEEE Computer graphics and applications},
  volume={20},
  number={5},
  pages={20--27},
  year={2000},
  publisher={IEEE},
  doi={10.1109/38.865875}
}