Journal of Computational and Applied Mathematics
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We consider the finite element solution of the parameterized semilinear elliptic equation $\Delta u + \lambda u + u^{5} = 0, u 0$, where $u$ is defined in the unit cube and is 0 on the boundary of the cube. This equation is important in analysis, and it is known that there is a value $\lambda_{0} 0$ such that no solutions exist for $\lambda u which is supported by the numerical calculations. The asymptotic methods also give sharp estimates both for the error in the finite element solution when $\lambda \lambda_{0}$ and for the form of the spurious numerical solutions which are known to exist when $\lambda