Abstract
AbstractIn this paper, we introduce an $$H({\text {div}})$$
H
(
div
)
finite element method on polygonal and polyhedral meshes for solving the Stokes equations in the primary velocity–pressure formulation. An $$H({\text {div}})$$
H
(
div
)
finite element on polygons or polyhedra is introduced to approximate the velocity so that the method is pressure robust and produces exact divergence free solutions, when the discontinuous $$P_k$$
P
k
finite element is adopted for the pressure approximation. In addition, this method is stabilizer-free, in handling the $$H^1$$
H
1
non-conformity. Optimal order error estimates are established for the method. Numerical tests are conducted to confirm the theory.
Publisher
Springer Science and Business Media LLC