A multiscale method for semilinear elliptic equations (Q931006)

The authors study a multiscale method for semilinear elliptic equations. They introduce the model problem and recall the basic theory of upper and lower solutions. A multiscale method based on the method of upper and lower solutions is provided in detail and the error estimate between the exact solution and the asymptotic expansion of order one is presented. Based on these results the authors verify the error estimates between the exact solution and the approximation by multiscale method. Some numerical examples validating the theory discussed are presented.