@article{discovery1476860,
            year = {2015},
           title = {A monotonicity preserving, nonlinear, finite element upwind method for the transport equation},
         journal = {Applied Mathematics Letters},
           pages = {141--146},
          volume = {49},
           month = {November},
            note = {{\copyright} 2015. This manuscript version is published under a Creative Commons Attribution Non-commercial Non-derivative 4.0 International licence (CC BY-NC-ND 4.0). This licence allows you to share, copy, distribute and transmit the work for personal and non-commercial use providing author and publisher attribution is clearly stated. Further details about CC BY licences are available at http://creativecommons.org/licenses/by/4.0.},
             url = {http://dx.doi.org/10.1016/j.aml.2015.05.005},
        abstract = {We propose a simple upwind finite element method that is monotonicity preserving and weakly consistent of order O(h3/2). The scheme is nonlinear, but since an explicit time integration method is used the added cost due to the nonlinearity is not prohibitive. We prove the monotonicity preserving property for the forward Euler method and for a second order Runge-Kutta method. The convergence properties of the Runge-Kutta finite element method are verified on a numerical example.},
            issn = {1873-5452},
          author = {Burman, E},
        keywords = {Stabilized finite element method; Shock capturing; Flux correction; Monotonicity preserving; Transport equation}
}