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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| Veröffentlicht in: | Journal of scientific computing 2024, Vol.101 (1), p.11, Article 11 |
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| creator | Dolejší, Vít Shin, Hyun-Geun Vlasák, Miloslav |
| description | 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. |
| doi_str_mv | 10.1007/s10915-024-02650-x |
| format | Article |
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hp
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hp
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hp
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| 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 |
| title | Error Estimates and Adaptivity of the Space-Time Discontinuous Galerkin Method for Solving the Richards Equation |
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