A local discontinuous Galerkin scheme for Darcy flow with internal jumps

作者：Rupp Andreas^*; Knabner Peter; Dawson Clint

来源：Computational Geosciences, 2018, 22(4): 1149-1159.

DOI：10.1007/s10596-018-9743-7

• Local discontinuous Galerkin method
• Instationary Darcy problem
• Jump condition
• Henry's Law
• Different orders of approximation spaces

We present a new version of the local discontinuous Galerkin method which is capable of dealing with jump conditions along a submanifold I"(LG) (i.e., Henry's Law) in instationary Darcy flow. Our analysis accounts for a spatially and temporally varying, non-linear permeability tensor in all estimates which is also allowed to have a jump at I"(LG) and gives a convergence order result for the primary and the flux unknowns. In addition to this, different approximation spaces for the primary and the flux unknowns are investigated. The results imply that the most efficient choice is to choose the degree of the approximation space for the flux unknowns one less than that of the primary unknown. The only stabilization in the proposed scheme is represented by a penalty term in the primary unknown.

• 出版日期2018-8