Work

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

Year: 2024

Type: article

Abstract: 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.

Source: Journal of Scientific Computing

DOI: 10.1007/s10915-024-02650-x

Authors: Vít Dolejší, Hyun-Geun Shin, Miloslav Vlasák

Institutions: Charles University, Czech Technical University in Prague

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Univerzita Karlova v Praze, Grantová Agentura České Republiky, FP7 Ideas: European Research Council