Work

Elliptic Reconstruction and A Posteriori Error Estimates for Parabolic Variational Inequalities

Year: 2024

Type: preprint

Abstract: Elliptic reconstruction property, originally introduced by Makridakis and Nochetto for linear parabolic problems, is a well-known tool to derive optimal a posteriori error estimates. No such results are known for nonlinear and nonsmooth problems such as parabolic variational inequalities (VIs). This article establishes the elliptic reconstruction property for parabolic VIs and derives a posteriori error estimates in $L^{\infty}(0,T;L^{2}(Ω))$. The estimator consists of discrete complementarity terms and standard residual. As an application, the residual-type error estimates are presented.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2402.17724

Authors: Antil, Harbir, Khandelwal, Rohit

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Office of Naval Research, Air Force Office of Scientific Research

Awards: G1090354770, Algorithms and Numerical Methods for Optimization with Partial Differential Equation Constraints, G1523888516, G3327059554, G6098521345, G8876996369

OpenAlex ID: W4392271672

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