"A posteriori" error indicator and error estimators for adaptive mesh refinement

• K.C. Chellamuthu ^[1] ; Nathan Ida ^[1]
  1. [1] University of Akron

     University of Akron

     City of Akron, Estados Unidos

     
• Localización: Compel: International journal for computation and mathematics in electrical and electronic engineering, ISSN 0332-1649, Vol. 14, Nº 2-3, 1995, págs. 139-156
• Idioma: inglés
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• Resumen

  • Two different ‘a posteriori’ error estimation techniques are proposed in this paper. The effectiveness of the error estimates in adaptive mesh refinement for 2D and 3D electrostatic problems are also analyzed with numerical test results. The post‐processing method employs an improved solution to estimate the error, whereas the gradient of field method utilizes the gradient of the field solution for estimating the ‘a posterior’ error. The gradient of field method is computationally inexpensive, since it solves a local problem on a patch of elements. The error estimates are tested by solving a set of self‐adjoint boundary value problems in 2D and 3D using a hierarchical minimal tree based mesh refinement algorithm. The numerical test results and the performance evaluation establish the effectiveness of the proposed error estimates for adaptive mesh refinement.