Applied Mathematics & Information Sciences

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This work is devoted to the study of the finite element method for a class of nonlocal elliptic problems associated with p- Kirchhoff-type operator. The convergence and a priori error estimates for the discrete formulation are established. Moreover, the finite element formulation is nonlinear, it can then be solved by Newton-Raphson’s iterative but the main issue is that the Jacobian matrix of the Newton-Raphson method is full due to the presence of the nonlocal term thereby making computation expensive. To avoid this difficulty, the new formulation whose Jacobian matrix is sparse is given. Finally, the predictions observed theoretically are validated by means of numerical experiments.

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