The patch test as a validation of a new finite element for the solution of convection-diffusion equations Original Research Article

A first goal of this work is to show how the patch test, a well-known tool established in the field of continuum mechanics, can be fruitfully employed to demonstrate the convergence and robustness of a numerical method for the solution of convection dominated flow problems. A new finite element passing the patch test is then proposed for the discrestization of current continuity equations in semiconductors. Numerical results relative to the study of two-dimensional devices are included to validate the effectiveness of the method.