Linear Robin-type Domain Decomposition scheme for Mixed Formulation of Richards' Equation
Abstract
In this work, we present a linear Robin-type domain decomposition scheme for solving the mixed formulation of Richards' equation (mLRDD-scheme), governing flow in variably saturated porous media. Assuming a highly heterogeneous porous medium consisting of multiple blocks/layers of distinct materials, we apply non-overlapping domain decomposition to isolate individual materials, yielding near-homogeneous conditions within each subdomain. Richards' equation is discretized in time by backward Euler and linearized using the L-scheme. A Robin-type interface condition, consistent with the mixed formulation, is then derived to couple the subdomains. For spatial discretization, mixed finite elements are employed, ensuring local mass conservation and providing the flux variables consistent with the Robin condition. The convergence of the proposed scheme is rigorously proved. Heterogeneous, multidomain numerical examples in 2D/3D are presented to demonstrate the efficiency and robustness of the scheme, along with numerical validation of the theoretical convergence results.
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BibTeX
@misc{synnevag2026linear,
title = {{Linear Robin-type Domain Decomposition scheme for Mixed Formulation of Richards' Equation}},
author = {Åsmund v. B. Synnevåg and Wietse M. Boon and Florin A. Radu and Sarah E. Gasda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26478},
eprint = {2609.26478},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26478},
}
RIS
TY - UNPB
TI - Linear Robin-type Domain Decomposition scheme for Mixed Formulation of Richards' Equation
AU - Åsmund v. B. Synnevåg
AU - Wietse M. Boon
AU - Florin A. Radu
AU - Sarah E. Gasda
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26478
UR - https://arxiv.org/abs/2609.26478
AB - In this work, we present a linear Robin-type domain decomposition scheme for solving the mixed formulation of Richards' equation (mLRDD-scheme), governing flow in variably saturated porous media. Assuming a highly heterogeneous porous medium consisting of multiple blocks/layers of distinct materials, we apply non-overlapping domain decomposition to isolate individual materials, yielding near-homogeneous conditions within each subdomain. Richards' equation is discretized in time by backward Euler and linearized using the L-scheme. A Robin-type interface condition, consistent with the mixed formulation, is then derived to couple the subdomains. For spatial discretization, mixed finite elements are employed, ensuring local mass conservation and providing the flux variables consistent with the Robin condition. The convergence of the proposed scheme is rigorously proved. Heterogeneous, multidomain numerical examples in 2D/3D are presented to demonstrate the efficiency and robustness of the scheme, along with numerical validation of the theoretical convergence results.
ER -