Derivation and model error analysis of multidimensional time dependent solute transport models
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We derive multi-dimensional coupled time-dependent models from three-dimensional systems of solute transport in given evolving domains and their surroundings. Such models enable the efficient computation of averaged solute concentrations in large networks of blood vessels surrounded by perivascular spaces in the brain parenchyma. Thus, our models provide an important tool to simulate brain transport of solutes. We show the existence and uniqueness of solutions for all the coupled models including the full three-dimensional system. The modelling error introduced by the derivation's assumptions is analysed via establishing a priori error estimates in suitable Bochner spaces. Further, we prove error estimates for a continuous finite element discretisation for the coupled 3D-1D models. Numerical tests verify our theoretical findings.