### Electronic Research Archive

2021, Issue 5: 3405-3427. doi: 10.3934/era.2021045
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# An adjoint-based a posteriori analysis of numerical approximation of Richards equation

• Received: 01 November 2020 Revised: 01 April 2021 Published: 24 June 2021
• Primary: 65M60, 65M08; Secondary: 65Z05

• 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.

Citation: Victor Ginting. An adjoint-based a posteriori analysis of numerical approximation of Richards equation[J]. Electronic Research Archive, 2021, 29(5): 3405-3427. doi: 10.3934/era.2021045

### Related Papers:

• 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. ###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142 1.604 0.8

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