ABSTRACT
The finite element method (FEM) is a computer-based approximate way of finding solutions to differential equations. An approximate way of seeking solutions to partial differential equations (PDEs) and ordinary differential equations will inherently introduce errors. Thus, FEM results will always contain errors. There are several different types of errors in FEM, such as modeling error, user error, and program error. This chapter discusses in detail the modeling errors. The most challenging cause for errors is when framing the problem becomes difficult. This type of error is often categorized as the problem-framing error, and it occurs when the PDE or the constraining conditions do not capture the actual situation of the problem at hand due to required simplifications in formulating the problem. The chapter uses a quantitative example to illustrate the effect of mesh refinement on the convergence of FEM solutions.
