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Department of Mathematics,
University of California San Diego

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Center for Computational Mathematics Seminar

Zhaolong Han

UCSD

T-coercive Mixed Finite Element Methods for Nonlocal Saddle Point Problems

Abstract:

Mixed finite element methods are widely used in numerical partial differential equations. By introducing an auxiliary variable, a second-order PDE can be rewritten as a first-order linear system, enabling more robust discretizations than the original formulation. However, such discretizations typically rely on discrete inf–sup conditions for the finite element spaces, which can be difficult to verify. A remedy is the T-coercivity approach: construct a bijective linear operator T that transforms the saddle point problem into a coercive one. In this talk, I will present a T-coercive framework for designing stable mixed finite elements for nonlocal saddle-point problems, along with convergence theory and numerical experiments. We establish convergence as the nonlocal horizon tends to zero and/or as the discretization parameter vanishes.

October 28, 2025

11:00 AM

APM 2402 & Zoom ID 975 1565 7226

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