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Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG [Abstract]: The valuation problem of renewable energy certificates can be formulated in terms of a nonlinear PDE model where the underlying stochastic factors are the accumulated green certificates sold by an authorized producer and the natural logarithm of the renewable generation rate. In the present paper, the nonlinear convective term is treated with the Bermúdez–Moreno duality method for maximal monotone operators as in Baamonde-Seoane et al. (2021). The main novelty of this article comes from the proposed techniques for the numerical solution of the resulting linear problem. In this case, we propose a Lagrange–Galerkin method which mainly consists of Crank–Nicolson characteristics for time discretization combined with finite elements for the discretization in the accumulated green certificates and the natural logarithm of the renewable generation rate directions. Finally, several numerical examples are presented to illustrate the good performance of the method and model, and its comparison with other numerical schemes employed to solve the same problem. Xunta de Galicia; ED431C 2018/033 Xunta de Galicia; ED431C 2022/47 Xunta de Galicia; ED431G 2019/01 The authors acknowledge the funding by Spanish MINECO with the grants MTM2016-76497-R and PID2019-10858RB-I00, and by Galician Government, Spain with the grants ED431C 2018/033 and ED431C 2022/47, both including FEDER financial support. As members of CITIC, they also acknowledge the grant ED431G 2019/01, funded by Consellería de Educación, Spain , Universidade e Formación Profesional of Xunta de Galicia through FEDER funds with 80%, from FEDER Galicia 2014–2020 Program and 20% from Secretaría Xeral de Universidades. |
