Abstract
The Petrov–Galerkin finite-element method with a lumped mass matrix is analyzed. It is stated that in some cases it excessively smoothes the solutions and causes large errors. It is shown that weight functions can be chosen, which eliminate the above-mentioned drawbacks. The corresponding approximations are constructed in the form of systems of ordinary differential equations and finite-difference schemes. The theoretical results are confirmed by calculated data.
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Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2013, pp. 152–163.
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Siryk, S.V. Analysis of lumped approximations in the finite-element method for convection–diffusion problems. Cybern Syst Anal 49, 774–784 (2013). https://doi.org/10.1007/s10559-013-9565-5
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DOI: https://doi.org/10.1007/s10559-013-9565-5