## Abstract

An L^{2} least-squares finite element method for second-order elliptic problems having non-symmetric diffusion coefficient matrix in two- and three-dimensional bounded domains is proposed and analyzed. The main result is the coercivity estimate of the bilinear form associated with the least-squares functional, which is established by using more direct techniques than that in Ref. [7]. It is proved that the method is not subject to the Ladyzhenskaya-Babuška-Brezzi condition and that the finite element approximation yields a symmetric positive definite linear system with condition number O(h^{-2}). Optimal error estimates in the H^{1}(Ω) × H(div; Ω) norm are derived. An equivalent a posteriori error estimator in the above norm is described. Some concluding remarks are also given.

Original language | English |
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Pages (from-to) | 419-432 |

Number of pages | 14 |

Journal | Numerical Functional Analysis and Optimization |

Volume | 23 |

Issue number | 3-4 |

DOIs | |

State | Published - May 2002 |

## Keywords

- A posteriori error estimates
- A priori error estimates
- Elliptic problems
- Finite element methods
- Least squares