### Abstract

Let k be a sequence of triangulations of a polyhedron n and let S k be the associated finite element space of continuous, piecewise polynomials of degree m . Let u k S k be the finite element approximation of the solution u of a second-order, strongly elliptic system Pu = f with zero Dirichlet boundary conditions. We show that a weak approximation property of the sequence S k ensures optimal rates of convergence for the sequence u k . The method relies on certain a priori estimates in weighted Sobolev spaces for the system Pu = 0 that we establish. The weight is the distance to the set of singular boundary points. We obtain similar results for the Poisson problem with mixed Dirichlet-Neumann boundary conditions on a polygon.

Original language | English (US) |
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Pages (from-to) | 613-639 |

Number of pages | 27 |

Journal | Numerical Functional Analysis and Optimization |

Volume | 26 |

Issue number | 6 |

DOIs | |

State | Published - Sep 1 2005 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Signal Processing
- Computer Science Applications
- Control and Optimization

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## Cite this

*Numerical Functional Analysis and Optimization*,

*26*(6), 613-639. https://doi.org/10.1080/01630560500377295