Abstract
Many problems in science and engineering can be rigorously recast into minimizing a suitable energy functional. We have been develo** efficient and flexible solution strategies to tackle various minimization problems by employing finite element discretization with P1 triangular elements [1, 2]. An extension to rectangular hp-finite elements in 2D is introduced in this contribution.
A. Moskovka and J. Valdman announce the support of the Czech Science Foundation (GACR) through the grant 21-06569K. M. Frost acknowledges the support of the Czech Science Foundation (GACR) through the grant 22-20181S.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Matonoha, C., Moskovka, A., Valdman, J.: Minimization of p-Laplacian via the finite element method in MATLAB. In: Lirkov, I., Margenov, S. (eds.) LSSC 2021. LNCS, vol. 13127, pp. 496–503. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97549-4_61
Moskovka, A., Valdman, J.: Fast MATLAB evaluation of nonlinear energies using FEM in 2D and 3D: nodal elements. Appl. Math. Comput. 424, 127048 (2022)
Drozdenko, D., Knapek, M., Kruvzík, M., Máthis, K., et al.: Elastoplastic deformations of layered structures. Milan J. Math. 90, 691–706 (2022)
Frost, M., Valdman, J.: Vectorized MATLAB implementation of the incremental minimization principle for rate-independent dissipative solids using FEM: a constitutive model of shape memory alloys. Mathematics 10, 4412 (2022)
Szabó, B., Babuška, I.: Finite Element Analysis. Wiley, New York (1991)
Szabó, B., Babuška, I.: Introduction to Finite Element Analysis. Wiley, New York (2011)
Moskovka, A., Valdman, J.: MATLAB implementation of HP finite elements on rectangles using hierarchical basis functions. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K. (eds.) PPAM 2022. LNCS, vol. 13827, pp. 287–299. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-30445-3_24
Conn, A.R., Gould, N.I.M., Toint, P.L.: Trust-Region Methods. SIAM, Philadelphia (2000)
Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. SIAM, Philadelphia (2002)
Lindqvist, P.: Notes of the p-Laplace equation (sec. ed.), report 161 of the Department of Mathematics and Statistics, University of Jyväskylä, Finland (2017)
Marsden, J.E., Hughes, T.J.: Mathematical Foundations of Elasticity. Prentice-Hall, Englewood Cliffs (1983)
Innerberger, M., Praetorius, D.: MooAFEM: an object oriented MATLAB code for higher-order adaptive FEM for (nonlinear) elliptic PDEs. Appl. Math. Comput. 442, 127731 (2023)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Frost, M., Moskovka, A., Valdman, J. (2024). Minimization of Energy Functionals via FEM: Implementation of hp-FEM. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computations. LSSC 2023. Lecture Notes in Computer Science, vol 13952. Springer, Cham. https://doi.org/10.1007/978-3-031-56208-2_31
Download citation
DOI: https://doi.org/10.1007/978-3-031-56208-2_31
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-56207-5
Online ISBN: 978-3-031-56208-2
eBook Packages: Computer ScienceComputer Science (R0)