An adjoint-based a posteriori analysis of numerical approximation of Richards equation
DOI10.3934/era.2021045zbMath1478.65085OpenAlexW3176872255MaRDI QIDQ2055174
Publication date: 3 December 2021
Published in: Electronic Research Archive (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/era.2021045
a posteriori error estimationadjoint methodsRichards equationfinite volume elementspace-time finite element
Flows in porous media; filtration; seepage (76S05) Finite volume methods applied to problems in fluid mechanics (76M12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Applications to the sciences (65Z05) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)
Cites Work
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- Adaptive multistep time discretization and linearization based on a posteriori error estimates for the Richards equation
- A mass-conservative control volume-finite element method for solving Richards' equation in heterogeneous porous media
- The finite volume method for Richards equation
- Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality
- A finite volume element method for a non‐linear elliptic problem
- Galerkin-Type Approximations which are Discontinuous in Time for Parabolic Equations in a Variable Domain
- A Posteriori Error Bounds and Global Error Control for Approximation of Ordinary Differential Equations
- Finite Volume Methods for Elliptic PDE's: A New Approach
- CAPILLARY CONDUCTION OF LIQUIDS THROUGH POROUS MEDIUMS
- Estimating the error of numerical solutions of systems of reaction-diffusion equations
- Error estimates in $L^2$, $H^1$ and $L^\infty$ in covolume methods for elliptic and parabolic problems: A unified approach
- Computational Methods for Multiphase Flows in Porous Media
- A posteriori analysis of a space and time discretization of a nonlinear model for the flow in partially saturated porous media