A p-adaptive three dimensional boundary element method for elastostatic problems using quasi-Lagrange interpolation

An adaptive method for the determination of the order of element (or element order) was developed for the boundary element analysis of 3D elastostatic problems using quasi-Lagrange interpolation. Here the order of element means the highest order of polynomial function, which interpolates the displacement distribution in element. This method was based on acquiring the desired accuracy for each boundary element. From the numerical experiments, the relation ξ=k(1/p)^β was deduced, where ξ is the error of the result of the boundary element analysis relative to the exact value, p is the order of element, and k and β are constants.Applying this relation to the two results of computations with different orders of element, the order of element for the third computation was deduced. A computer program using this adaptive determination method for the order of element was developed and applied to several 3D elastostatic problems of various shapes. The usefulness of the method was illustrated by these application results.