Numerical approximation of equations involving minimal/maximal operators by successive solution of obstacle problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:342

Article

Agnelli, J. P.¹  Kaufmann, U.²  Rossi, J. D.³ 

[1] Univ Nacl Cordoba, FaMAF CIEM, Medina Allende S-N, RA-5000 Cordoba, Argentina

[2] Univ Nacl Cordoba, FaMAF, Medina Allende S-N, RA-5000 Cordoba, Argentina

[3] Univ Buenos Aires, Dept Matemat, Ciudad Univ,Pab 1, RA-1428 Buenos Aires, DF, Argentina

关键词: Maximal operators;    Numerical approximations;    Obstacle problems;   

DOI  :  10.1016/j.cam.2018.04.016

来源: Elsevier

【 摘 要 】

Let Omega subset of R-2 be a polygonal domain, and let L-i, i= 1,2, be two elliptic operators of the form L(i)u(x) := -div(A(i)(x)Delta u(x) + c(i)(x)u(x) - f(i)(x). Motivated by the results in Blanc et al. (2016), we propose a numerical iterative method to compute the numerical approximation to the solution of the minimal problem {min{L(1)u, L(2)u} = 0 in Omega, u= 0 on partial derivative Omega. The convergence of the method is proved, and numerical examples illustrating our results are included. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free