Work

Adaptive approximations of inclusions in a semilinear elliptic problem related to cardiac electrophysiology

Year: 2025

Type: article

Abstract: In this work, we investigate the numerical reconstruction of inclusions in a semilinear elliptic equation arising in the mathematical modeling of cardiac ischemia. We propose an adaptive finite-element method for the resulting constrained minimization problem that is relaxed by a phase-field approach. The a posteriori error estimators of the adaptive algorithm consist of three components, i.e., the state variable, the adjoint variable and the complementary relation. Moreover, using tools from adaptive finite-element analysis and nonlinear optimization, we establish the strong convergence for a subsequence of adaptively generated discrete solutions to a solution of the continuous optimality system. Several numerical examples are presented to illustrate the convergence and efficiency of the adaptive algorithm.

Source: IMA Journal of Numerical Analysis

Authors: Bangti Jin, Fengru Wang, Yifeng Xu

Institutions: Chinese University of Hong Kong, Shanghai Normal University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Science and Technology Commission of Shanghai Municipality, Shanghai Normal University, Chinese University of Hong Kong

Awards: G3865785182, G440906136, G467015429, G5017780471, G540381957

OpenAlex ID: W4411728111