The applications of a finite element scheme to one-dimensional linear advection-diffusion equation, the incompressible Navier-Stokes equations, and compressible Euler system of equations are presented. The mesh-based scheme is the Petrov-Galerkin weak formulation with exponential weighting functions. Some numerical results demonstrate the workability and the validity of the present approach.
Kakuda, K., Maeda, Y. (2010). Finite element-based flow simulations using exponential weighting functions. The International Conference on Computational & Experimental Engineering and Sciences, 14(1), 37–42. https://doi.org/10.3970/icces.2010.014.037
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