# zbMATH — the first resource for mathematics

First-order system least squares for velocity-vorticity-pressure form of the Stokes equations, with application to linear elasticity. (English) Zbl 0856.76010
Summary: We study the least-squares method for the generalized Stokes equations (including linear elasticity) based on the velocity-vorticity-pressure formulation in $$d=2$$ or 3 dimensions. The least-squares functional is defined in terms of the sum of the $$L^2$$- and $$H^{-1}$$-norms of the residual equations, but weighted appropriately by the Reynolds number (Poisson ratio). Our approach for establishing ellipticity of the functional does not use Agmon-Douglis-Nirenberg theory, but is founded more on basic principles. We also analyze the case where the $$H^{-1}$$-norm in the functional is replaced by a discrete $$H^{-1}$$-norm to make the computation feasible. We show that the resulting algebraic equations can be preconditioned by well-known techniques uniformly well in the Reynolds number (Poisson ratio).

##### MSC:
 76D07 Stokes and related (Oseen, etc.) flows 74B05 Classical linear elasticity 35Q30 Navier-Stokes equations 35Q72 Other PDE from mechanics (MSC2000)
Full Text: