On Least-Squares Finite Element Methods for the Poisson Equation and Their Connection to the Dirichlet and Kelvin Principles

@article{Bochev2005OnLF,
  title={On Least-Squares Finite Element Methods for the Poisson Equation and Their Connection to the Dirichlet and Kelvin Principles},
  author={Pavel B. Bochev and Max Gunzburger},
  journal={SIAM J. Numerical Analysis},
  year={2005},
  volume={43},
  pages={340-362}
}
Least-squares finite element methods for first-order formulations of the Poisson equation are not subject to the inf-sup condition and lead to stable solutions even when all variables are approximated by equal-order continuous finite element spaces. For such elements, one can also prove optimal convergence in the “energy” norm (equivalent to a norm on H1(Ω) × H(Ω, div)) for all variables and optimal L2 convergence for the scalar variable. However, showing optimal L2 convergence for the flux has… CONTINUE READING
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