Koondanibha Mitra: Thursday 26 November at 16:00 via this link
Richards equation is commonly used to model the flow of water and air through the soil, and serves as a gateway equation for multiphase flow through porous domains. It is a nonlinear advection-reaction-diffusion equation that exhibits both elliptic-parabolic and hyperbolic-parabolic kind of degeneracies. In this study, we provide fully computable, locally space-time efficient, and reliable a posteriori error bounds for numerical solutions of the fully degenerate Richards equation. This is achieved in a variation of the $ H^1(H^{-1})\cap L^2(L^2) \cap L^2(H^1)$ norm characterized by the minimum regularity inherited by the exact solutions. For showing global reliability, a non-local in time error estimate is derived individually for the $H^1(H^{-1})$, $L^2(L^2)$ and the $L^2(H^1)$ error components with a maximum principle and a degeneracy estimator being used for the last one. Local and global space-time efficient error bounds are obtained, and error contributors such as flux and time non-conformity, quadrature, linearisation, data oscillation, are identified and separated. The estimates hold also in space-time adaptive settings. The predictions are verified numerically and it is shown that the estimators correctly identify the errors up to a factor in the order of unity.
