ENH : ALE formulation one-dimensional about msc-literature-review HOT 1 CLOSED

From 2019_arbitraryLagrangianEulerianTypeFiniteElementMethodsFormulationPdEsTimeDependentDomainsVanishingDiscreteSpaceConservationLaw_ivancic:

Also, there is more room in choosing the method of calculating of the grid velocity without (essentially) changing the formulation of the problem, thus making the coding easily adjustable. Implementation-wise, everything is kept on the original reference configuration and consequently introduces some additional differential operators in order to transform the space derivatives from the current configuration onto the reference one. We believe this approach offers a few advantages ahead of the implementation on the current configuration (of course, under the assumption that the two approaches are equivalent on the discrete level which will be argued later). Among them, we mention three here. The first two lie in the fact that the reference domain is fixed in time. Then the test/basis function spaces will be time independent and the finite element spaces do not need to be updated at each time step. The third, keeping everything on the reference configuration, the evolution of the domain is kept in the Jacobians of the ALE map thus making the connection between the domain time dependency and all the terms in the differential equation more clear. In cases when a weak formulation is posed on the current configuration, the only explicit connection between the domain time dependency and the under the integral terms is through the domain velocity which appears in the form of convective terms.

In fact, my thesis regarding ROMs on moving domains has to do with the fact that those Jacobians are not always easy to obtain.

from msc-literature-review.