Error Estimates and Adaptivity of the Space-Time Discontinuous Galerkin Method for Solving the Richards Equation

We present a higher-order space-time adaptive method for the numerical solution of the Richards equation that describes a flow motion through variably saturated media. The discretization is based on the space-time discontinuous Galerkin method, which provides high stability and accuracy and can natu...

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Bibliographic Details
Published in:Journal of scientific computing 2024, Vol.101 (1), p.11, Article 11
Main Authors: Dolejší, Vít, Shin, Hyun-Geun, Vlasák, Miloslav
Format: Article
Language:English
Subjects:
Adaptation
Algorithms
Approximation
Computational Mathematics and Numerical Analysis
Estimates
Galerkin method
Hydraulics
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Spacetime
Theoretical
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Summary:We present a higher-order space-time adaptive method for the numerical solution of the Richards equation that describes a flow motion through variably saturated media. The discretization is based on the space-time discontinuous Galerkin method, which provides high stability and accuracy and can naturally handle varying meshes. We derive reliable and efficient a posteriori error estimates in the residual-based norm. The estimates use well-balanced spatial and temporal flux reconstructions which are constructed locally over space-time elements or space-time patches. The accuracy of the estimates is verified by numerical experiments. Moreover, we develop the hp -adaptive method and demonstrate its efficiency and usefulness on a practically relevant example.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-024-02650-x