A posteriori error analysis with applications to finite element methodology and finite difference methodology

摘要

A problem of continued interest for many years has been the capacitance of the regular polyhedra. A new numerical value for each of these regular solids is presented, obtained by employing a finite difference technique. In addition, the theory of an established method is presented for computing point-wise truncation error estimates a posteriori. This method is applied to the capacitance solution of two of the regular polyhedra, the tetrahedron and the cube, to give point-wise error estimates for the solution. A new technique for extending the error analysis method to finite element methodology is introduced and applications given for plane structural problems on a clamped plate and a cantilevered plate. The latter of these problems involves mixed boundary conditions, which are rarely addressed by error analysis methods. An important feature of the error analysis method presented is that the results do not require the solution of a higher order h or p version.