A posteriori error estimates for fourth-order elliptic problems

✍ Scribed by Slimane Adjerid

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 181 KB
• Volume: 191
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(01)00412-1

✦ Synopsis

for estimating the finite element discretization error to fourth-order elliptic problems. We show how to construct a posteriori error estimates from jumps of the third partial derivatives of the finite element solution when the finite element space consists of piecewise polynomials of odd-degree and from the interior residuals for even-degree approximations on meshes of square elements. These estimates are shown to converge to the true error under mesh refinement. We also show that these a posteriori error estimates are asymptotically correct for more general finite element spaces. Computational results from several examples show that the error estimates are accurate and efficient on rectangular meshes.