Open AccessAn adjoint-based a posteriori analysis of numerical approximation of Richards equation
Author(s) -
Victor Ginting
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021045
Subject(s) - mathematics , discretization , finite element method , galerkin method , linearization , estimator , adjoint equation , a priori and a posteriori , dimension (graph theory) , discontinuous galerkin method , variable (mathematics) , nonlinear system , mathematical analysis , temporal discretization , partial differential equation , philosophy , epistemology , quantum mechanics , physics , statistics , pure mathematics , thermodynamics
This paper formulates a general framework for a space-time finite element method for solving Richards Equation in one spatial dimension, where the spatial variable is discretized using the linear finite volume element and the temporal variable is discretized using a discontinuous Galerkin method. The actual implementation of a particular scheme is realized by imposing certain finite element space in temporal variable to the variational equation and appropriate "variational crime" in the form of numerical integrations for calculating integrations in the formulation. Once this is in place, adjoint-based error estimators for the approximate solution from the scheme is derived. The adjoint problem is obtained from an appropriate linearization of the nonlinear system. Numerical examples are presented to illustrate performance of the methods and the error estimators.