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Mathematics Colloquium

Beatrice Riviere
Rice University

Title:Analysis and Simulations of Multidimensional Coupled Problems
Date: Friday, March 1, 2024
Place and Time: Love 101, 3:05-3:55 pm

Abstract. Multidimensional coupled problems occur in several applications ranging from geosciences to biomedicine. Drug delivery from the vasculature to the organ, or solute clearance through the lymphatic vessels are two such examples of processes involving flow and transport in networks of 1D vessels embedded in a 3D domain. This talk will first discuss the mathematical and numerical analysis of elliptic partial differential equations with line source. The analysis of such problems is non-standard because the solution exhibits a logarithmic singularity near the 1D line. Convergence of a discontinuous Galerkin method is obtained. Second, we discuss applications of the coupled 3D-1D problems to flow in the liver. With the singularity removal approach, the solution is split into an explicit lower regularity part and a smooth part that can be solved numerically on a uniform mesh.