Stability of Discrete Stokes Operators in Fractional Sobolev Spaces

abstract

• Using a general approximation setting having the generic properties of finite-elements, we prove uniform boundedness and stability estimates on the discrete Stokes operator in Sobolev spaces with fractional exponents. As an application, we construct approximations for the time-dependent Stokes equations with a source term in L p (0, T; L q ()) and prove uniform estimates on the time derivative and discrete Laplacian of the discrete velocity that are similar to those in Sohr and von Wahl [20]. 2007 Birkhaueser.

authors

• Pasciak, Joseph

published proceedings

• JOURNAL OF MATHEMATICAL FLUID MECHANICS

author list (cited authors)

• Guermond, J., & Pasciak, J. E.

citation count

• 8

complete list of authors

• Guermond, Jean-Luc||Pasciak, Joseph E

publication date

• November 2008

publisher

• Springer Nature  Publisher

published in

• Journal of Mathematical Fluid Mechanics  Journal

keywords

• Bessel Potentials
• Finite Elements
• Navier-stokes Equations
• Negative Norms
• Pressure Estimates
• Stokes Operator

Digital Object Identifier (DOI)

• 10.1007/s00021-007-0244-z

start page

• 588

end page

• 610

volume

• 10

issue

• 4

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2Fs00021-007-0244-z