Summary
In this paper, we consider monotone explicit iterations of the finite element schemes for the nonlinear equations associated with the boundary value problem Δu=bu 2, based on piecewise linear polynomials and the lumping operator. These iterations construct the monotonically decreasing and increasing sequences, and convergence proofs are given. Finally, we present some numerical examples verifying the effectiveness of the theory.
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Ishihara, K. Monotone explicit iterations of the finite element approximations for the nonlinear boundary value problem. Numer. Math. 43, 419–437 (1984). https://doi.org/10.1007/BF01390183
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DOI: https://doi.org/10.1007/BF01390183