A General Error Estimate For Parabolic Variational Inequalities

DOI10.1515/CMAM-2021-0050arXiv2009.09607MaRDI QIDQ6349505

Publication date: 21 September 2020

Abstract: The gradient discretisation method (GDM) is a generic framework designed recently, as a discretise in spatial space, to partial differential equations. This paper aims to use the GDM to establish a first general error estimate for numerical approximations of parabolic obstacle problems. This gives the convergence rates of several well--known conforming and non conforming numerical methods. Numerical experiments based on the hybrid finite volume method are provided to verify the theoretical results.

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Numerical analysis (65-XX) Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators (35K86)

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