Adaptive refinement criterion for elliptic problems discretized by FEM

STORTI MARIO; NIGRO NORBERTO; IDELSOHN, SERGIO

COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING

John Wiley and sons

Lugar: Hoboken, New Jersey; Año: 1993 vol. 9 p. 729 - 743

1069-8299

In a recent paper1 we presented a data structure to be used with multigrid techniques on non-homogeneously refined FEM meshes. This paper focuses on the adaptive refinement techniques used there. The error estimate is obtained from standard Taylor series. For each element we compute its efficiency in terms of the size, the norm of the second derivatives of the unknown and the parameter p, where Lp is the chosen norm. The way the norm influences the optimal mesh is studied. The number of elements to be refined at each step is such to produce a fast convergence to the optimal mesh, followed by successive homogeneous refinements. We hope that the analysis of these two subjects could be of value for people working with other (perhaps very dissimilar) adaptive refinement techniques (error estimate and data structure, for instance).