Abstract
A error estimate for the finite element solutions of elliptic boundary value problems is introduced. The error measure is defined by the energy-norm distance between the kinematically admissible stress field computed by the displacement finite element method, and a quasi-statically admissible stress field. The error estimate is defined using this distance normalized by the total strain energy of the deformed body. The element contribution to the above error estimate is used to define an error indicator and a local error measure which can be used in adaptive finite element method as a criteria for mesh refinement. This method of error estimate can be implemented in existing finite element programs in a straightforward manner.
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