Optimal error estimates of the diffuse domain method for second order parabolic equations.

Wenrui Hao, Lili Ju, Yuejin Xu

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Article in BIT. Numerical mathematics, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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5 · Who and what money

Authors and funding

3 authors.

Wenrui HaoDepartment of mathematics, Pennsylvania State University, College Park, 16802 PA USA.

Lili JuDepartment of Mathematics, University of South Carolina, Columbia, 29208 USA.

Yuejin XuDepartment of mathematics, Pennsylvania State University, College Park, 16802 PA USA.

Funding

A pathophysiology driven spatial dynamic modeling framework for personalized prediction and precision medicineR35GM146894 · NIGMS · PENNSYLVANIA STATE UNIVERSITY, THE · PI WENRUI HAO · 2022 to 2026

$2.0M

NIGMS NIH HHS R35 GM146894

6 · The paper itself

Abstract

In this paper, we study the convergence behavior of the diffuse domain method (DDM) for solving a class of second-order parabolic partial differential equations with Neumann boundary condition posed on general irregular domains. The DDM employs a phase-field function to extend the original parabolic problem to a similar but slightly modified problem defined over a larger rectangular domain that contains the target physical domain. Based on the weighted Sobolev spaces, we rigorously establish the convergence of the diffuse domain solution to the original solution as the interface thickness parameter goes to zero, together with the corresponding optimal error estimates under the weighted

Indexed as

Diffuse domain methodError estimatesIrregular domainsParabolic equationsWeighted norms

Identifiers

PMID41924075

DOI10.1007/s10543-026-01118-8

PMCPMC13035889

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