发表机构
Jagiellonian University in Krakow; Universidad Austral; CONICET, Argentina（克拉科夫雅盖隆大学; 南方大学; 阿根廷国家科学研究委员会）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对带混合边界条件的稳态热传导半变分不等式，提出有限元逼近方法，证明网格尺寸趋于零与罚参数趋于无穷时离散解的双重极限强收敛，并给出最优阶误差估计与数值验证。
AI 中文摘要
本文研究具有混合边界条件的稳态热传导问题的数值逼近与收敛性分析。该物理模型由依赖于传热参数 $\alpha > 0$ 的半变分不等式控制。我们考虑该罚问题的有限元逼近，以及其对应的极限问题，后者在部分边界上规定常数温度。主要理论结果确立了离散解的强收敛性。具体而言，我们证明了当网格尺寸 $h$ 趋于零且罚参数 $\alpha$ 趋于无穷大时，有限元逼近对极限解的双重极限收敛，且这两个极限过程独立且同时进行。我们进一步通过离散极限问题的最优阶误差估计补充了收敛性分析，并解释了为何无法期望关于罚参数的一致估计。理论结果通过四个由制造解方法验证的数值算例加以说明。
英文摘要
In this paper we study the numerical approximation and convergence analysis of a steady-state heat conduction problem with mixed boundary conditions. The physical model is governed by a hemivariational inequality depending on a heat transfer parameter $α> 0$. We consider the finite element approximation of this penalized problem, as well as its corresponding limit problem with a prescribed constant temperature on a part of the boundary. The main theoretical result establishes the strong convergence of the discrete solutions. Specifically, we prove the double-limit convergence of the finite element approximations to the limit solution as the mesh size $h$ tends to zero and the penalization parameter $α$ tends to infinity, independently and simultaneously. We further complement the convergence analysis with an error estimate of optimal order for the discrete limit problem, and we explain why an estimate uniform in the penalization parameter cannot be expected. The theoretical results are illustrated by numerical simulations on four examples verified by the method of manufactured solutions.
Comments24 pages, 6 figures, 2 tables
Journal refNonlinear Anal. RWA 95 (2027) 104769
DOI：10.1016/j.nonrwa.2026.104769
