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We analyse a PDE system modelling poromechanical processes (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes in the medium. We investigate the well-posedness of the nonlinear set of equations using fixed-point theory, Fredholms alternative, a priori estimates, and compactness arguments. We also propose a mixed finite element method and rigorously demonstrate the stability of the scheme. Error estimates are derived in suitable norms, and numerical experiments are conducted to illustrate the mechano-chemical coupling and to verify the theoretical rates of convergence.
We provide a preliminary comparison of the dispersion properties, specifically the time-amplification factor, the scaled group velocity and the error in the phase speed of four spatiotemporal discretization schemes utilized for solving the one-dimens
A study is presented on the convergence of the computation of coupled advection-diffusion-reaction equations. In the computation, the equations with different coefficients and even types are assigned in two subdomains, and Schwarz iteration is made b
We perform the linear stability analysis for a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes convected in
In this paper, by employing the asymptotic method, we prove the existence and uniqueness of a smoothing solution for a singularly perturbed Partial Differential Equation (PDE) with a small parameter. As a by-product, we obtain a reduced PDE model wit
We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection-diffusion-reaction equations based on the CORSING (COmpRessed SolvING) paradigm. Combining the Petrov-Galerkin technique with the compr