A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition
We use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are also satisfied exactly. Moreover, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Conventional techniques to improve conservation such as the addition of artificial weights or redundant terms like ∇ × v = 0, are no longer necessary. The final system of equations is a mixture of a finite volume scheme (differential equations) and a higher order finite element method (constitutive relations). Numerical experiments confirm the spectral accuracy of the method and its local conservation, .