## Abstract

In this article we apply the subdomain-Galerkin/least squares method, which is first proposed by Chang and Gunzburger for first-order elliptic systems without reaction terms in the plane, to solve second-order non-selfadjoint elliptic problems in two- and three-dimensional bounded domains with triangular or tetrahedral regular triangulations. This method can be viewed as a combination of a direct cell vertex finite volume discretization step and an algebraic least-squares minimization step in which the pressure is approximated by piecewise linear elements and the flux by the lowest order Raviart-Thomas space. This combined approach has the advantages of both finite volume and least-squares methods. Among other things, the combined method is not subject to the Ladyzhenskaya-Babuška-Brezzi condition, and the resulting linear system is symmetric and positive definite. An optimal error estimate in the H^{1}(Ω) X H(div; Ω) norm is derived. An equivalent residual-type a posteriori error estimator is also given.

Original language | English |
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Pages (from-to) | 738-751 |

Number of pages | 14 |

Journal | Numerical Methods for Partial Differential Equations |

Volume | 18 |

Issue number | 6 |

DOIs | |

State | Published - Nov 2002 |

## Keywords

- Error estimates
- Finite volume methods
- Least-squares methods
- Mixed elliptic problems
- Raviart-Thomas spaces