Parameters correction of an elliptical equation using an a posteriori estimate

Abstract

In nature several phenomena touch humanity to act and control these phenomena we try to model their evolution. To simplify the study of the equations obtained, most of the time we try to use linear forms and in this way modelling errors are made which can influence the correct analysis of these phenomena. In this work we focus on the Richards' equation, where the coefficients changes their forms from a given value hs: This value is unknown then the coefficients are approximated. We prove an a priori and an a posteriori estimates on the modelling error. This estimates allows us, using local indicators, to build an adaptive algorithm to control the modelling error and automatically determine the "best" approximation of hs. Numerical results confirm theconvergence of this procedure and the interest of this approach.