| Abstract: |
| \begin{abstract}
We present an \emph{a priori} error analysis for a fully discrete, parallelizable, explicitly coupled splitting scheme for fluid--poroelastic structure interaction problems modeled by the time-dependent Stokes--Biot system. The method decouples the fluid and poroelastic subproblems in a fully explicit manner, enabling the two systems to be solved independently at each time step while consistently enforcing the interface conditions. This structure makes the scheme computationally efficient and well suited for partitioned implementations.
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The analysis is carried out within a discrete energy framework. We introduce Ritz-type projections in the fluid and poroelastic subdomains and compare the fully discrete scheme with a time-discrete continuous formulation. This yields reduced error equations in which the leading interpolation terms cancel, leaving only consistency errors associated with temporal discretization and lagged interface data arising from the explicit splitting. Using these reduced equations, we derive a discrete error energy identity and establish unconditional error estimates in a combined energy--dissipation norm through a Gronwall-type argument. The resulting bounds prove first-order accuracy in time and optimal convergence in space, with rates determined by the polynomial degree of the finite element spaces. Numerical experiments based on manufactured solutions confirm the theoretical results, showing first-order temporal convergence for all variables and optimal spatial convergence rates.
\end{abstract} |
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