Issue |
ESAIM: M2AN
Volume 59, Number 1, January-February 2025
|
|
---|---|---|
Page(s) | 43 - 71 | |
DOI | https://doi.org/10.1051/m2an/2024062 | |
Published online | 08 January 2025 |
Lowest-order nonstandard finite element methods for time-fractional biharmonic problem
1
Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, Maharashtra 400076, India
2
Université Paul Sabatier Toulouse III & CNRS, Institut de Mathématiques, 31062 Toulouse Cedex 9, France
3
Indian Institute of Technology Bombay, Mumbai, Maharashtra 400076, India
* Corresponding author: neela@math.iitb.ac.in; nataraj.neela@gmail.com
Received:
22
November
2023
Accepted:
26
July
2024
In this work, we consider an initial-boundary value problem for a time-fractional biharmonic equation in a bounded polygonal domain with a Lipschitz continuous boundary in ℝ2 with clamped boundary conditions. After stating the well-posedness, we focus on some regularity results of the solution with respect to the regularity of the problem data. The spatially semidiscrete scheme covers several popular lowest-order piecewise-quadratic finite element schemes, namely, Morley, discontinuous Galerkin, and C0 interior penalty methods, and includes both smooth and nonsmooth initial data. Optimal order error bounds with respect to the regularity assumptions on the data are proved for both homogeneous and nonhomogeneous problems. The numerical experiments validate the theoretical convergence rate results.
Mathematics Subject Classification: 35R11 / 65M15 / 65M60
Key words: Time-fractional equation / biharmonic / lowest-order FEM / smooth and nonsmooth initial data / semidiscrete / error estimates
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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