First order system least squares method for the interface problem of the Stokes equations
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- First order system least squares method for the interface problem of the Stokes equations
- Hessari, Peyman
- First order system least squares method; Interface problem; Spectral collocation method; Stokes equation
- Issue Date
- PERGAMON-ELSEVIER SCIENCE LTD
- COMPUTERS & MATHEMATICS WITH APPLICATIONS, v.68, no.3, pp.309 - 324
- The first order system least squares method for the Stokes equation with discontinuous viscosity and singular force along the interface is proposed and analyzed. First, interface conditions are derived. By introducing a physical meaningful variable such as the velocity gradient, the Stokes equation transformed into a first order system of equations. Then the continuous and discrete norm least squares functionals using Legendre and Chebyshev weights for the first order system are defined. We showed that continuous and discrete homogeneous least squares functionals are equivalent to appropriate product norms. The spectral convergence of the proposed method is given. A numerical example is provided to support the method and its analysis.
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