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The superconvergent patch recovery (SPR) and adaptive finite element refinement. (English) Zbl 0779.73078

Summary: The error estimation processes which have been developed by the authors [Int. J. Numer. Methods Eng. 33, No. 7, 1331-1364 (1992; Zbl 0769.73084); and ibid. 33, No. 7, 1365-1382 (1992; Zbl 0769.73085)] depend on the accuracy with which stresses (gradients) can be recovered. The recovery methods available currently, such as the \(L_ 2\) projection and averaging, are inaccurate, and an improved process is needed. This paper presents a very much improved recovery process yielding superconvergent values throughout the domain. Details of this method, named the superconvergent patch recovery, are presented with test results showing its efficiency. Examples of adaptive, \(h\)-based refinement are given, showing high local and overall efficiency indices for error estimation.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74B10 Linear elasticity with initial stresses
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