Numerical evaluation of FEM with application to the 1D advection-diffusion problem
We present a numerical procedure to evaluate the efficiency of finite element numerical methods. We improve some of the ideas proposed in previous works, and we give a theoretical and empirical justification in a general framework. The proposed procedure performs an eigenvalue computation, and requires the knowledge of the behavior of the exact operator in order to choose proper norms for the evaluations. In the experiments we focus our attention on the 1D advection-diffusion problem: we show that our numerical procedure gives actually very sharp indications about the optimality of the tested numerical methods.
KeywordsSaddle Point Problem Empirical Justification Eigenvalue Computation Standard Finite Element Method Sharp Indication
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