Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/115441
Title: | Nonlinear systems of parabolic IBVP: A stable super-supraconvergent fully discrete piecewise linear FEM | Authors: | Carvalho, S. Ferreira, J. A. Pena, G. |
Keywords: | Finite difference method; Finite element method; Nonuniform grid; Error analysis; Sunspot simulation | Issue Date: | Apr-2022 | Publisher: | Elsevier | Project: | UIDB/00324/2020 SFRH/BD/107894/2015 |
Serial title, monograph or event: | Applied Mathematics and Computation | Volume: | 419 | Abstract: | The main purpose of this paper is the design of discretizations for second order nonlinear parabolic initial boundary value problems which are stable and present second order of convergence with respect to H1-discrete norms. The convergence results are established assuming that the solutions are in H3. The stability analysis of numerical methods around a numerical solution requires the uniform boundness of such solution. Although such bounds are usually taken as an assumption, in this paper these will be deduced as a corollary of suitable error estimates. As the methods can be simultaneously seen as piecewise linear finite element methods and finite difference methods, the convergence results can be seen simultaneously as superconvergence results and supraconvergence results. Numerical results illustrating the sharpness of the smoothness assumptions and an application to simulation of the solar magnetic field in the umbra (the central zone of a sunspot) are also included. | URI: | https://hdl.handle.net/10316/115441 | ISSN: | 0096-3003 | DOI: | 10.1016/j.amc.2021.126857 | Rights: | closedAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais I&D CMUC - Artigos em Revistas Internacionais |
Files in This Item:
File | Description | Size | Format | Login |
---|---|---|---|---|
2022_Carvalho_Ferreira_Pena.pdf | 2.3 MB | Adobe PDF | Request a copy |
Page view(s)
75
checked on Oct 9, 2024
Download(s)
2
checked on Oct 9, 2024
Google ScholarTM
Check
Altmetric
Altmetric
This item is licensed under a Creative Commons License