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dc.contributor.authorAmrein, Mario-
dc.contributor.authorHeid, Pascal-
dc.contributor.authorWihler, Thomas P.-
dc.date.accessioned2023-06-15T14:27:17Z-
dc.date.available2023-06-15T14:27:17Z-
dc.date.issued2023-
dc.identifier.issn0036-1429de_CH
dc.identifier.issn1095-7170de_CH
dc.identifier.urihttps://digitalcollection.zhaw.ch/handle/11475/28059-
dc.description.abstractWe 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.de_CH
dc.language.isoende_CH
dc.publisherSociety for Industrial and Applied Mathematicsde_CH
dc.relation.ispartofSIAM Journal on Numerical Analysisde_CH
dc.rightsLicence according to publishing contractde_CH
dc.subjectAdaptive finite element methodde_CH
dc.subjectSteady statede_CH
dc.subjectEnergy minimizationde_CH
dc.subjectFixed-point iterationde_CH
dc.subject.ddc510: Mathematikde_CH
dc.titleA numerical energy reduction approach for semilinear diffusion-reaction boundary value problems based on steady-state iterationsde_CH
dc.typeBeitrag in wissenschaftlicher Zeitschriftde_CH
dcterms.typeTextde_CH
zhaw.departementSchool of Management and Lawde_CH
zhaw.organisationalunitInstitut für Risk & Insurance (IRI)de_CH
dc.identifier.doi10.1137/22M1478586de_CH
zhaw.funding.euNode_CH
zhaw.issue2de_CH
zhaw.originated.zhawYesde_CH
zhaw.pages.end783de_CH
zhaw.pages.start755de_CH
zhaw.publication.statuspublishedVersionde_CH
zhaw.volume61de_CH
zhaw.publication.reviewPeer review (Publikation)de_CH
zhaw.author.additionalNode_CH
zhaw.display.portraitYesde_CH
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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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