Easy Use of Error Measures in ADINA

A very important step in finite element analysis is to ensure that the numerical results are accurate. The error measures based on the work of Sussman and Bathe (see T. Sussman and K. J. Bathe, "Studies of Finite Element Procedures — On Mesh Selection", Computers & Structures, Vol. 21, pp. 257-264, 1985) can be very useful in this regard, and moreover, these error measures can be easily used in ADINA.

We demonstrated the use of the error estimation available in ADINA already in our News of June 15, 2006, where we also gave some general thoughts regarding the task of measuring errors.

We want to show in the present News how easy it is to use the error estimation feature in ADINA: just click the icon for Error Plots in the Results Toolbar of the ADINA User Interface (AUI).^*

Below we show the error estimates obtained using the Error Plots icon for a contact problem solved with the ADINA automatic 'Total load application (TLA) scheme'. We calculated the exact error by comparing the coarse mesh solution with an extremely fine mesh solution. Of course, this calculation would not be done in practice. Like in the June 15, 2006 News, using the coarse mesh solution, we see that the error estimation has given a conservative estimate. These estimates are useful in assessing whether a finer mesh should be used.

Figure 1: Contact Between a Block and a Rigid Cylinder — Schematic

Figure 2: Contact Between a Block and a Rigid Cylinder; Coarse Mesh is Shown

Figure 3: Coarse Mesh Solution

Figure 4: Normalized Estimated Error

Figure 5: Normalized Exact Error

Keywords:
Error measure, error estimator, error indicator, meshing, mesh refinement, reliability