Abstract
We begin this section with a warning. We discuss here the viscous Burgers equation as an approximation to the Navier–Stokes equation in one space dimension. In order to focus on a mixed formulation considering a finite-element analysis in space and a finite-difference analysis in time that will be accessible to students at the beginning graduate level who have not yet mastered the functional analysis required for the resulting treatment, the following presentation contains no consideration of the necessary functional framework. In other words, we discuss only formal features of the variational formulations and numerical implementation of the finite-element analysis.
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References
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Chaskalovic, J. (2014). Nonlinear Problems. In: Mathematical and Numerical Methods for Partial Differential Equations. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-03563-5_7
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DOI: https://doi.org/10.1007/978-3-319-03563-5_7
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