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https://hdl.handle.net/10316/115442
Title: | FDM/FEM for nonlinear convection–diffusion–reaction equations with Neumann b.oundary conditions—Convergence analysis for smooth and nonsmooth solutions | Authors: | Ferreira, J. A. Pena, G. |
Keywords: | Finite difference method; Finite element method; Nonuniform grid; Error analysis; Nonlinear convection–diffusion–reaction; Homogeneous Neumann boundary conditions | Issue Date: | Aug-2024 | Project: | UIDB/00324/2020 | Serial title, monograph or event: | Journal of Computational and Applied Mathematics | Volume: | 446 | Abstract: | This paper aims to present in a systematic form the stability and convergence analysis of a numerical method defined in nonuniform grids for nonlinear elliptic and parabolic convection– diffusion–reaction equations with Neumann boundary conditions. The method proposed can be seen simultaneously as a finite difference scheme and as a fully discrete piecewise linear finite element method. We establish second convergence order with respect to a discrete 𝐻1 norm which shows that the method is simultaneously supraconvergent and superconvergent. Numerical results to illustrate the theoretical results are included. | URI: | https://hdl.handle.net/10316/115442 | ISSN: | 0377-0427 | DOI: | 10.1016/j.cam.2024.115866 | Rights: | closedAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais I&D CMUC - Artigos em Revistas Internacionais |
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2024_Ferreira_Pena.pdf | 704.29 kB | Adobe PDF | Request a copy |
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