The finite element method with continuity constraints for stair-step grids in geoscience

摘要

This work investigates the enforcement of continuity constraints on stair-step grids which are specialized grids for simulations in geosciences. They are rectilinear in horizontal directions but locally discontinuous (i.e., noncon-forming) in the vertical direction. Furthermore, they allow for (partly) collapsed elements in order to model pinched-out layers. A robust and efficient algorithm for enforcing continuity is proposed which is tailored to the special properties of stair-step grids. A number of two- and three-dimensional finite element method (FEM) simulations on stair-step grids are conducted. Thereby, the Lagrange multiplier and penalty method with different ansatz spaces are studied for pointwise and averaged constraints. A particu-lary useful choice is the penalty method with continuous constraints and penalty parameters that depend on the element size.