%0 Journal Article %1 Kröker2012441 %A Kröker, I. %A Rohde, C. %D 2012 %J Applied Numerical Mathematics %K hyperbolic multiplicative-noise myown %N 4 %P 441 - 456 %R http://dx.doi.org/10.1016/j.apnum.2011.01.011 %T Finite volume schemes for hyperbolic balance laws with multiplicative noise %U http://www.sciencedirect.com/science/article/pii/S016892741100033X %V 62 %X We consider finite volume schemes for a scalar stochastic balance law with multiplicative noise. For a class of monotone numerical fluxes we establish the pathwise convergence of a semi-discrete finite volume solution towards a stochastic entropy solution. Main tool is a stochastic version of the compensated compactness approach. The approach relies solely on L p -estimates. It avoids the use of a maximum principle and total-variation estimates. These are typical tools in the deterministic case but are not available for the non-deterministic model. Numerical results illustrate the analytical findings.

@article{Kröker2012441, abstract = {We consider finite volume schemes for a scalar stochastic balance law with multiplicative noise. For a class of monotone numerical fluxes we establish the pathwise convergence of a semi-discrete finite volume solution towards a stochastic entropy solution. Main tool is a stochastic version of the compensated compactness approach. The approach relies solely on L p -estimates. It avoids the use of a maximum principle and total-variation estimates. These are typical tools in the deterministic case but are not available for the non-deterministic model. Numerical results illustrate the analytical findings. }, added-at = {2016-04-26T10:34:30.000+0200}, author = {Kröker, I. and Rohde, C.}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2fbdb6c6af9777516523af2681bbede3a/ik}, doi = {http://dx.doi.org/10.1016/j.apnum.2011.01.011}, interhash = {64860e369eaa4c497300fa7d8ca256c6}, intrahash = {fbdb6c6af9777516523af2681bbede3a}, issn = {0168-9274}, journal = {Applied Numerical Mathematics }, keywords = {hyperbolic multiplicative-noise myown}, note = {Third Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE 2010) }, number = 4, pages = {441 - 456}, timestamp = {2016-04-26T08:35:20.000+0200}, title = {Finite volume schemes for hyperbolic balance laws with multiplicative noise }, url = {http://www.sciencedirect.com/science/article/pii/S016892741100033X}, volume = 62, year = 2012 }