| Publication type: | Article in scientific journal |
| Type of review: | Peer review (publication) |
| Title: | A numerical energy reduction approach for semilinear diffusion-reaction boundary value problems based on steady-state iterations |
| Authors: | Amrein, Mario Heid, Pascal Wihler, Thomas P. |
| et. al: | No |
| DOI: | 10.1137/22M1478586 |
| Published in: | SIAM Journal on Numerical Analysis |
| Volume(Issue): | 61 |
| Issue: | 2 |
| Page(s): | 755 |
| Pages to: | 783 |
| Issue Date: | 2023 |
| Publisher / Ed. Institution: | Society for Industrial and Applied Mathematics |
| ISSN: | 0036-1429 1095-7170 |
| Language: | English |
| Subjects: | Adaptive finite element method; Steady state; Energy minimization; Fixed-point iteration |
| Subject (DDC): | 510: Mathematics |
| Abstract: | We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems, where the nonlinear reaction terms need to be neither monotone nor convex. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy reduction approach. More specifically, this procedure aims to generate a sequence of numerical approximations, which results from the iterative solution of related (stabilized) linearized discrete problems, and tends to a critical point of the underlying energy functional in a stable way. Simultaneously, the finite-dimensional approximation spaces are adaptively refined. This is implemented in terms of a new mesh refinement strategy in the context of finite element discretizations, which again relies on the energy structure of the problem under consideration. In particular, in contrast to more traditional approaches, it does not involve any a posteriori error estimators, and is based on local energy reduction indicators instead. In combination, the resulting adaptive algorithm consists of an iterative linearization procedure on a sequence of hierarchically refined discrete spaces, which we prove to converge toward a solution of the continuous problem in an appropriate sense. Numerical experiments demonstrate the robustness and reliability of our approach for a series of examples. |
| URI: | https://digitalcollection.zhaw.ch/handle/11475/28059 |
| Fulltext version: | Published version |
| License (according to publishing contract): | Licence according to publishing contract |
| Departement: | School of Management and Law |
| Organisational Unit: | Institute for Risk & Insurance (IRI) |
| Appears in collections: | Publikationen School of Management and Law |
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Amrein, M., Heid, P., & Wihler, T. P. (2023). A numerical energy reduction approach for semilinear diffusion-reaction boundary value problems based on steady-state iterations. SIAM Journal on Numerical Analysis, 61(2), 755–783. https://doi.org/10.1137/22M1478586
Amrein, M., Heid, P. and Wihler, T.P. (2023) ‘A numerical energy reduction approach for semilinear diffusion-reaction boundary value problems based on steady-state iterations’, SIAM Journal on Numerical Analysis, 61(2), pp. 755–783. Available at: https://doi.org/10.1137/22M1478586.
M. Amrein, P. Heid, and T. P. Wihler, “A numerical energy reduction approach for semilinear diffusion-reaction boundary value problems based on steady-state iterations,” SIAM Journal on Numerical Analysis, vol. 61, no. 2, pp. 755–783, 2023, doi: 10.1137/22M1478586.
AMREIN, Mario, Pascal HEID und Thomas P. WIHLER, 2023. A numerical energy reduction approach for semilinear diffusion-reaction boundary value problems based on steady-state iterations. SIAM Journal on Numerical Analysis. 2023. Bd. 61, Nr. 2, S. 755–783. DOI 10.1137/22M1478586
Amrein, Mario, Pascal Heid, and Thomas P. Wihler. 2023. “A Numerical Energy Reduction Approach for Semilinear Diffusion-Reaction Boundary Value Problems Based on Steady-State Iterations.” SIAM Journal on Numerical Analysis 61 (2): 755–83. https://doi.org/10.1137/22M1478586.
Amrein, Mario, et al. “A Numerical Energy Reduction Approach for Semilinear Diffusion-Reaction Boundary Value Problems Based on Steady-State Iterations.” SIAM Journal on Numerical Analysis, vol. 61, no. 2, 2023, pp. 755–83, https://doi.org/10.1137/22M1478586.
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