Abstract
An original h-adaptive finite element method (FEM) scheme is proposed
for the axisymmetric problem of the linear theory of elasticity, based on a comparison of
stresses computed by the FEM and the indirect boundary element method (IBEM). A
FEM variant with approximations on bilinear serendipity quadrilaterals and an IBEM
variant based on linear boundary elements are used. To ensure local mesh refinement
at non-matching interfaces, the FEM with mortar functions is applied. The proposed
mesh refinement indicator is defined through the elementwise root-mean-square difference
between the stresses obtained by FEM and IBEM. Numerical experiments for a problem
with a known analytical solution and for an L-shaped domain have shown that the
introduced indicator can be used as a practical refinement indicator for h-adaptive FEM
mesh refinement, while its potential use as an a posteriori error estimator requires further
theoretical justification.