A linear potential reconstruction technique based on Raviart-Thomas basis functions for cell-centered finite volume approximations to the Darcy problem
DOI:
https://doi.org/10.5540/03.2025.011.01.0332Keywords:
potential reconstruction, gradient reconstruction, error estimation, lowest-order Raviart-Thomas basis functionsAbstract
We propose a technique to recover linear potentials from the solution obtained from cell-centered finite volume approximations to the scalar elliptic problem, i.e., the cell-centered potentials and the normal fluxes on the edges. The technique employs lowest-order Raviart-Thomas basis functions to compute a local potential gradient, which is then used to obtain nodal potentials and from there a global energy-conforming potential. Numerical convergence tests in two dimensions show that the gradient of the reconstructed potential converges at O(h), outperforming reconstructions obtained via averaging of cell-centered values and producing similar results compared to a quadratic reconstruction technique.
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