Discrete vector potential representation of a divergence-free vector field in three-dimensional domains: numerical analysis of a model problem
Dubois, François
HAL, hal-00660366 / Harvested from HAL
Text on HAL
For the representation of a divergence-free vector field defined on a bounded simply connected three-dimensional domain of with a smooth boundary by its curl and its normal component on the boundary, a mixed formulation also involving a vector potential is proposed. The vector fields are discretized with help of curved finite elements that are conforming in H(div) or H(curl). A discrete gauge condition is proposed to assume the uniqueness of the stream function. Optimal error estimates are derived, and a numerical experiment is presented.
Publié le : 1990-10-04
Classification:  mixed finite elements,  curved boundaries,  discrete gauge condition,  65N30,  [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] 
@article{hal-00660366,
     author = {Dubois, Fran\c cois},
     title = {Discrete vector potential representation of a divergence-free vector field in three-dimensional domains: numerical analysis of a model problem},
     journal = {HAL},
     volume = {1990},
     number = {0},
     year = {1990},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00660366}
}

Dubois, François. Discrete vector potential representation of a divergence-free vector field in three-dimensional domains: numerical analysis of a model problem. HAL, Tome 1990 (1990) no. 0, . http://gdmltest.u-ga.fr/item/hal-00660366/