Abstract
The finite-element method is one of the widely used numerical methods, but there seems to be no research on the accuracy of various kinds of deformed elements used in this method. One of the authors has proposed a correction method for the finite-element method for the one-dimensional and the two-dimensional convection-diffusion equations using the error analysis technique. Through this error analysis technique, we can estimate the numerical accuracy for various kinds of deformed elements in the finite-element formulation. In this study, we estimated the theoretical error for concentrated elements, mixed elements of triangular elements and rectangular elements, and deformed elements for the two-dimensional convection-diffusion equation. The Galerkin formulation and the modified Galerkin formulation are considered in the finite-element formulation. Finally, we confirmed the general correspondence between the error analysis results and the numerical simulation results.
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