Barth, Andrea; Stein, Andreas Numerical analysis for time-dependent advection-diffusion problems with random discontinuous coefficients. (English) Zbl 1501.65065 ESAIM, Math. Model. Numer. Anal. 56, No. 5, 1545-1578 (2022). MSC: 65M60 65M22 65N30 60H25 60H30 60H35 35R60 58J65 35K10 76S05 74A15 62C10 PDFBibTeX XMLCite \textit{A. Barth} and \textit{A. Stein}, ESAIM, Math. Model. Numer. Anal. 56, No. 5, 1545--1578 (2022; Zbl 1501.65065) Full Text: DOI arXiv
Stein, Andreas; Barth, Andrea A multilevel Monte Carlo algorithm for parabolic advection-diffusion problems with discontinuous coefficients. (English) Zbl 07240108 Tuffin, Bruno (ed.) et al., Monte Carlo and quasi-Monte Carlo methods. MCQMC 2018. Proceedings of the 13th international conference on Monte Carlo and quasi-Monte Carlo methods in scientific computing, Rennes, France, July 1–6, 2018. Cham: Springer. Springer Proc. Math. Stat. 324, 445-466 (2020). MSC: 65C05 PDFBibTeX XMLCite \textit{A. Stein} and \textit{A. Barth}, Springer Proc. Math. Stat. 324, 445--466 (2020; Zbl 07240108) Full Text: DOI arXiv
Barth, Andrea; Fuchs, Franz G. Uncertainty quantification for linear hyperbolic equations with stochastic process or random field coefficients. (English) Zbl 1372.65013 Appl. Numer. Math. 121, 38-51 (2017). MSC: 65C30 65C05 35R60 60H15 60H35 90B20 65M06 65M08 PDFBibTeX XMLCite \textit{A. Barth} and \textit{F. G. Fuchs}, Appl. Numer. Math. 121, 38--51 (2017; Zbl 1372.65013) Full Text: DOI arXiv
Barth, Andrea; Fuchs, Franz G. Uncertainty quantification for hyperbolic conservation laws with flux coefficients given by spatiotemporal random fields. (English) Zbl 1416.65288 SIAM J. Sci. Comput. 38, No. 4, A2209-A2231 (2016). MSC: 65M08 35L40 35L65 65C05 65M75 PDFBibTeX XMLCite \textit{A. Barth} and \textit{F. G. Fuchs}, SIAM J. Sci. Comput. 38, No. 4, A2209--A2231 (2016; Zbl 1416.65288) Full Text: DOI arXiv
Barth, Andrea; Lang, Annika Milstein approximation for advection-diffusion equations driven by multiplicative noncontinuous martingale noises. (English) Zbl 1260.60134 Appl. Math. Optim. 66, No. 3, 387-413 (2012). MSC: 60H35 60H15 65N30 PDFBibTeX XMLCite \textit{A. Barth} and \textit{A. Lang}, Appl. Math. Optim. 66, No. 3, 387--413 (2012; Zbl 1260.60134) Full Text: DOI Link
Barth, Andrea; Lang, Annika Multilevel Monte Carlo method with applications to stochastic partial differential equations. (English) Zbl 1270.65003 Int. J. Comput. Math. 89, No. 18, 2479-2498 (2012). Reviewer: Gong Guanglu (Beijing) MSC: 65C30 65C05 60G60 60H15 35R60 35K05 35L02 60H35 PDFBibTeX XMLCite \textit{A. Barth} and \textit{A. Lang}, Int. J. Comput. Math. 89, No. 18, 2479--2498 (2012; Zbl 1270.65003) Full Text: DOI
Barth, Andrea; Lang, Annika Simulation of stochastic partial differential equations using finite element methods. (English) Zbl 1255.60114 Stochastics 84, No. 2-3, 217-231 (2012). MSC: 60H35 60H15 60G60 65C30 PDFBibTeX XMLCite \textit{A. Barth} and \textit{A. Lang}, Stochastics 84, No. 2--3, 217--231 (2012; Zbl 1255.60114) Full Text: DOI
Barth, Andrea; Schwab, Christoph; Zollinger, Nathaniel Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients. (English) Zbl 1230.65006 Numer. Math. 119, No. 1, 123-161 (2011). Reviewer: Grigori N. Milstein (Yekaterinburg) MSC: 65C30 60H15 60H35 35R60 65C05 65Y20 PDFBibTeX XMLCite \textit{A. Barth} et al., Numer. Math. 119, No. 1, 123--161 (2011; Zbl 1230.65006) Full Text: DOI Link