Summary Selected finite element Eulerian-Lagrangian methods for the solution of the transport equation are compared systematically in the relatively simple context of 1D, constant coefficient, conservative problems. A combination of formal analysis and numerical experimentation is used to characterize the stability and accuracy that results from alternative treatments of the concentrations at the feet of the characteristic lines.
Exact integration leads to unconditional stability and excellent accuracy.
Quadrature integration leads only to conditional stability, but newly derived criteria show that stability restrictions are relatively mild and should not preclude the usefulness of quadrature integration methods in a range of practical applications. While conclusions cannot be extended directly to multiple dimensions and complex flows and geometries, results should provide useful insight to the development and behavior of specific Eulerian-Lagrangian transport models.