Document Zbl 08014706

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Nonlinear Sci. Numer. Simul.</a> <a href="/?q=in%3A526091" title="Articles in this Issue">143, Article ID 108632, 21 p. (2025)</a>. </div> <div class="abstract">Summary: This paper proposes and analyzes a type of efficient multigrid method, which is called multilevel correction method, for solving semilinear parabolic interface problems. The core idea of this method is that, at each time step, the semilinear elliptic interface problem’s solution is transformed into the same-scale linear elliptic interface problem’s solution in each level of multilevel space sequence and the semilinear elliptic interface problem’s solution on a newly defined low dimensional augmented subspace. Through analyzing the algebraic error estimate of the method, we design the method to iterate only one step in the intermediate grid layer, which makes our method more efficient than the work of <span class="zbmathjax-textit">F. Xu</span> et al. [Appl. Numer. Math. 179, 238–254 (2022; <a href="/1502.65258">Zbl 1502.65258</a>)] without losing accuracy. In addition, in the aspect of theoretical analysis, we present a new technique of analysis to derive the convergence order estimates. Numerical experiments are conducted to validate the precision and effectiveness of our proposed method.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M55" title="MSC2020">65M55</a> </td> <td class="space"> Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M15" title="MSC2020">65M15</a> </td> <td class="space"> Error bounds for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M60" title="MSC2020">65M60</a> </td> <td class="space"> Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Asemilinear+parabolic+interface+problem">semilinear parabolic interface problem</a>; <a href="/?q=ut%3Afinite+element+method">finite element method</a>; <a href="/?q=ut%3Anested+multilevel+correction+method">nested multilevel correction method</a>; <a href="/?q=ut%3Anonnested+multilevel+correction+method">nonnested multilevel correction method</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1502.65258">Zbl 1502.65258</a></div> <div class="software"> <h3>Software:</h3><a href="/software/1436">FreeFem++</a>; <a href="/software/4012">PETSc</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 08014706" data-ciurl="/ci/08014706" data-biburl="/bibtex/08014706.bib" data-amsurl="/amsrefs/08014706.bib" data-xmlurl="/xml/08014706.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/08014706.pdf" title="Zbl 08014706 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.cnsns.2025.108632" aria-label="DOI for “A type of efficient multigrid method for semilinear parabolic interface problems”" title="10.1016/j.cnsns.2025.108632">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Wang, Y.; Chen, Y.; Huang, Y.; Yi, H., A family of two-grid partially penalized immersed finite element methods for semi-linear parabolic interface problems, J Sci Comput, 88, 3, 39, 2021, Paper (80) · <a href="/1501.65060" class="nowrap">Zbl 1501.65060</a></td> </tr><tr> <td>[2]</td> <td class="space">De Cave, L. 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