... conservation, equilibrium of normal forces and the Beavers–Joseph–Saffman law. Since the meshes do not necessarily coincide, we use the Transfer Path Method to tie them. We establish the well-posedness of the method and provide error estimates where the influences of the nonconformity and the gap are explicit...

... ) Abstract In this paper a staggered mixed method based on the first-order system is proposed and analysed. The proposed method uses piecewise polynomial spaces enjoying partial continuity properties and hinges on a careful balancing of the involved finite element spaces. It supports polygonal meshes...

... or transformed in any way, and that the work properly cited. For commercial re-use, please contact [email protected] Abstract This work is concerned with the analysis of a space–time finite element discontinuous Galerkin method on polytopal meshes (XT-PolydG) for the numerical discretization of wave...

.... discontinuous Galerkin method thermo-hydro-mechanics thermo-poroelasticity nonlinear problems robustness polygonal and polyhedral meshes European Union 10.13039/501100000780 101115663 Italian Ministry of Universities and Research 20204LN5N5 Italian Research Center on High Performance...

... that may underlie divergence. adaptive design Aplysina fulva Aplysina cauliformis Caribbean coral reefs ecological function ecological speciation skeletal meshes sympatric congeners Phenotypic plasticity is a crucial aspect of the ecology and evolution of organisms...

... problems on general meshes, in dimensions 2 and 3. The resulting methods are unconditionally stable while preserving the small stencil typical of MPFA finite volumes. The key idea is to solve local variational problems with a well-designed stabilization term from which we deduce conservative flux instead...

... of a particular mesh construction—the tangential Delaunay complex—for that purpose. We then turn to manifold learning and argue that a variant of Isomap where the distances are instead computed on a reconstructed surface is minimax optimal for the isometric variant of the problem. shortest paths geodesic...

... important properties valid at the continuous level. In particular, it is possible to design discrete spaces with global high regularity, which preserve the polynomial divergence/curl, that is robust with respect to mesh-locking phenomena. Moreover, VEM can handle general polytopal meshes, which...

... general meshes nonlinear elliptic equation p-Laplacian coercivity consistency convergence 3D scheme Since more than twenty years, approximation of diffusion operators in the context of anisotropy and/or nonlinearity and/or general meshes was an important subject of research in numerical...

... and differentiation [ 25 ]. Therefore, it is reasonable to consider that the combination of such bioceramic scaffold and metal mesh may provide both good osteogenic capacity and reliable mechanical stability. Moreover, it is agreed that the pore architectures of porous scaffolds also play an important role...

... meshes. Pressure-robust methods are characterized by error estimates for the velocity that are fully independent of the pressure. A crucial question was left open in that work, namely whether the proposed construction could be extended to general polytopal meshes. In this paper, we provide a positive...

... the model reduces to the classical Fokker–Planck equation), a limit that presents practical importance. Concerning the error analysis, we obtain an optimal second-order accurate estimate for . A time-graded mesh is used to compensate for the singular behavior of the continuous solution near the origin...

... rotor, and in , and , respectively. Finally, for and , we define as the subspace of functions such that . The above couple of assumptions is the accepted standard in the VE literature (taking the role of the classical shape-regularity for tetrahedral meshes in finite...

... Steklov eigenvalue problem. The conforming VEM on polytopal meshes is used for discretization. We analyze the correct spectral approximation of the discrete scheme and prove an a priori error estimate for the discrete eigenvalues and eigenfunctions. The convergence order of a discrete eigenvalue...

...Manuel Solano; Sébastien Terrana; Ngoc-Cuong Nguyen; Jaime Peraire Fig. 2. Similar to Fig. 1 , but for the interface (black solid line) is interpolated by both meshes. A wide variety of methods for piecewise flat interfaces problems can be found in the literature, in contrast to those...

..., 1990 ), where least squares, mesh-dependent stabilization has been introduced. For general first-order systems, Monk & Richter (2005) introduced a DG space–time scheme based on numerical fluxes, which upwind in the transport direction. More recently, Trefftz DG methods, i.e., schemes employing...

... is a crucial component of the method proposed in this paper. To construct a topology graph, we first aim to resolve geometrical inconsistencies, such as duplicated elements, isolated vertices, degenerate elements, and self-intersections. This produces a mesh free from geometrical inconsistencies but still...

... to irrotational forces in the momentum balance. This paper argues that also divergence-free virtual element methods on polygonal meshes are not really pressure-robust as long as the right-hand side is not discretized in a careful manner. To be able to evaluate the right-hand side for the test functions, some...

... ) Abstract We design and analyze a hybrid high-order method on unfitted meshes to approximate the Stokes interface problem. The interface can cut through the mesh cells in a very general fashion. A cell-agglomeration procedure prevents the appearance of small cut cells. Our main results are inf-sup...

...Xiang Li; Gang Yao; Fenglin Niu; Di Wu Corresponding author: Gang Yao. E-mail: [email protected] 25 03 2020 13 10 2019 26 02 2020 immersed boundary method iterative symmetric interpolation irregular surface topography rectangular meshes finite-difference modelling The irregular...