[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86196-en":3,"doc-seo-86196-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},86196,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","Analysis-aware Interface Coarsening for Elliptic Problems Driven by an Equilibrated Flux Estimator","An a posteriori error estimator is developed for elliptic interface problems to drive analysis-aware interface coarsening based on an equilibrated flux reconstruction. The method targets interior-interface simplification that removes small features separating materials with different diffusion coefficients, reducing degrees of freedom while controlling accuracy. It decomposes the impact into modeling error from coarsening and numerical discretization error on the coarsened problem, localizes contributions on mesh elements, and tracks coefficient contrast explicitly. Reliability is proved and validated numerically, including full removal of an internal interface.","arXiv :2607 . 11297v1 [math .NA] 13 Jul 2026  \nAnalysis-aware interface coarsening for elliptic problems driven by an equilibrated flux estimator  \nDenise Grappein∗ Philipp Weder†  \nJuly 14, 2026  \nAbstract  \nWe propose an a posteriori error estimator that relies on an equilibrated flux reconstruction to enable analysis-aware interface coarsening decisions in elliptic interface problems. Interface coarsening consists of simplifying an internal interface that separates regions characterized by different physical properties in order to facilitate the meshing process and reduce the total number of degrees of freedom. This process extends the concept of defeaturing, where small features on the boundary of a computational domain are removed. Here, the features lie on an interior interface instead. The focus is on a Laplace problem with a discontinuous diffusion coefficient. The estimator accounts for both the modeling error arising from the interface coarsening and the numerical error from the discrete approximation of the solution to the coarsened-interface problem. It is localized on the mesh elements, and its constants explicitly track the contrast between the diffusion coefficients. The impact of different features can be assessed individually, yielding local contributions that indicate which features to coarsen and which to retain for a given mesh size. The use of an equilibrated flux reconstruction allows us to sharply bound the bulk numerical source of error. We prove the reliability of the estimator and verify it across several numerical examples, including the case where an internal interface is fully removed.  \n1 Introduction  \nThe geometric models appearing in engineering applications are often highly detailed, including features spanning multiple scales. This level of detail significantly increases the computational cost of numerical simulations by complicating mesh generation and increasing the number of degrees of freedom. The process of removing, prior to simulation, geometric features considered irrelevant to the accuracy of the solution of a given PDE is called defeaturing.  \nWhile defeaturing has historically been approached by exploiting a priori knowledge of the geometry and simulated physical processes [20, 21, 27], automated approaches require a quantitative, certified criterion to assess whether a given feature can be safely removed. This requirement has motivated the development of a posteriori defeaturing error estimators, capable of evaluating the impact of feature removal directly on the simplified geometry, without requiring the solution of the fully detailed problem.  \n∗ MOX, Department of Mathematics, Politecnico di Milano, Italy ([denise.grappein@polimi.it](denise.grappein@polimi.it)). Member of the GNCS INdAM group.  \n†Chair for Numerical Modelling and Simulation, École Polytechnique Fédérale de Lausanne (EPFL), Switzerland ([philipp.weder@epfl.ch](philipp.weder@epfl.ch)).  \nIn [10], a rigorous framework for analysis-aware defeaturing of the Poisson problem was introduced to address the case of boundary defeaturing. More precisely, it covers the removal of features on the exterior boundary subject to Neumann boundary conditions. The Dirichlet case is treated in [29], and [28] extends the estimates to quantities of interest other than the energy norm. Such defeaturing error estimators account for the modeling error introduced by neglecting each feature and can be combined with a classical a posteriori estimator of the discretization error to assess the relative importance of the two error contributions. In [9], this was done using a residual-based estimator, whereas in [12], an equilibrated flux error estimator was employed, with the advantage of yielding upper bounds free of unknown constants for the discretization error component. The resulting total-error estimators, accounting for both defeaturing and discretization errors, were used in [1, 11] as part of a comprehensive adaptive strategy that all","cbCais4j6HXg51a7","https://ap.wps.com/l/cbCais4j6HXg51a7","pdf",886137,1,19,"English","en",105,"# Abstract\n# Introduction","[{\"question\":\"What is the main goal of the proposed method?\",\"answer\":\"To enable analysis-aware coarsening of an interior interface in elliptic interface problems using an a posteriori error estimator driven by an equilibrated flux reconstruction.\"},{\"question\":\"How does the estimator handle errors in interface coarsening?\",\"answer\":\"It accounts for both modeling error introduced by coarsening and numerical error from the discrete approximation on the simplified-interface problem.\"},{\"question\":\"How can the method determine which interface features to remove or retain?\",\"answer\":\"The estimator localizes on mesh elements and provides feature-specific local contributions, indicating which features to coarsen and which to keep for a given mesh size.\"}]",1784209305,48,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"analysis-aware-interface-coarsening-for-elliptic-problems-driven-by-an-equilibrated-flux-estimator","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/analysis-aware-interface-coarsening-for-elliptic-problems-driven-by-an-equilibrated-flux-estimator/86196/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is the main goal of the proposed method?","Question",{"text":75,"@type":76},"To enable analysis-aware coarsening of an interior interface in elliptic interface problems using an a posteriori error estimator driven by an equilibrated flux reconstruction.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the estimator handle errors in interface coarsening?",{"text":80,"@type":76},"It accounts for both modeling error introduced by coarsening and numerical error from the discrete approximation on the simplified-interface problem.",{"name":82,"@type":73,"acceptedAnswer":83},"How can the method determine which interface features to remove or retain?",{"text":84,"@type":76},"The estimator localizes on mesh elements and provides feature-specific local contributions, indicating which features to coarsen and which to keep for a given mesh 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