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We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…

Numerical Analysis · Mathematics 2016-12-07 G. Manzini , K. Lipnikov , J. D. Moulton , M. Shashkov

Volume approximation is an important problem found in many applications of computer graphics, vision, and image processing. The problem is about computing an accurate and compact approximate representation of 3D volumes using some simple…

Graphics · Computer Science 2013-08-20 Feng Sun , Yi-King Choi , Yizhou Yu , Wenping Wang

Multidimensional population balance models (PBMs) describe chemical and biological processes having a distribution over two or more intrinsic properties (such as size and age, or two independent spatial variables). The incorporation of…

Computational Engineering, Finance, and Science · Computer Science 2025-04-29 Pavan Inguva , Richard D. Braatz

Only a few numerical methods can treat boundary value problems on polygonal and polyhedral meshes. The BEM-based Finite Element Method is one of the new discretization strategies, which make use of and benefits from the flexibility of these…

Numerical Analysis · Mathematics 2017-08-29 Steffen Weißer

The main contribution of this paper is the formulation of a diffuse approximation method(DAM), for two-dimensional channel flows. The proposed method is based on the vorticity-streamfunction formulation. The DAM which estimates derivates of…

Computational Physics · Physics 2018-11-19 Christian Prax , Hamou Sadat

In this study we have developed a flexible and efficient numerical scheme for the simulation of three-dimensional incompressible flows in spherical coordinates. The main idea, inspired by a similar strategy as (Verzicco, R., Orlandi, P.,…

Fluid Dynamics · Physics 2020-10-28 L. Santelli , P. Orlandi , R. Verzicco

The current paper presents a novel machinery for studying non-asymptotic minimax estimation of high-dimensional matrices, which yields tight minimax rates for a large collection of loss functions in a variety of problems. Based on the…

Statistics Theory · Mathematics 2013-06-18 Zongming Ma , Yihong Wu

A general, compact way of achieving second-order in finite-volume numerical methods is to perform a MUSCL-like, piecewise linear reconstruction of flow properties at each cell interface. To avoid the surge of spurious oscillations in the…

Fluid Dynamics · Physics 2026-02-13 Frederico Bolsoni Oliveira , João Luiz F. Azevedo

We study an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes using the CutFEM method. Our main contribution is the reconstruction of conservative fluxes from the CutFEM solution and their use in a…

Numerical Analysis · Mathematics 2025-07-11 Daniela Capatina , Aimene Gouasmi , Cuiyu He

Unstructured meshes are among the most versatile approaches for capturing non-canonical geometries in fluid dynamics simulations. Despite this, most high-fidelity first-principles phase-change models are developed and applied on structured…

Computational Physics · Physics 2026-04-17 Jan Kren , Bojan Ničeno , Yohei Sato

This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…

Numerical Analysis · Mathematics 2026-03-27 Stefan Frei , Tobias Knoke , Marc C. Steinbach , Anne-Kathrin Wenske , Thomas Wick

We analyze a semi-implicit finite volume scheme for the Gray--Scott system, a model for pattern formation in chemical and biological media. We prove unconditional well-posedness of the fully discrete problem and establish qualitative…

Numerical Analysis · Mathematics 2025-08-27 Tsiry Avisoa Randrianasolo

This paper deals with bounding the error on the estimation of quantities of interest obtained by finite element and domain decomposition methods. The proposed bounds are written in order to separate the two errors involved in the resolution…

Computational Physics · Physics 2015-02-11 Valentine Rey , Pierre Gosselet , Christian Rey

This paper investigates an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes, employing the CutFEM method. The main contribution is the a posteriori error analysis based on equilibrated fluxes belonging…

Numerical Analysis · Mathematics 2026-03-03 Daniela Capatina , Aimene Gouasmi

In this study, we present a parallel topology algorithm with a suitable interpolation method for chimera simulations in CFD. The implementation is done in the unstructured Finite Volume (FV) framework and special attention is given to the…

Fluid Dynamics · Physics 2023-05-29 Spiros Zafeiris , George Papadakis

After we derive the Serre system of equations of water wave theory from a generalized variational principle, we present some of its structural properties. We also propose a robust and accurate finite volume scheme to solve these equations…

Fluid Dynamics · Physics 2020-02-20 Denys Dutykh , Didier Clamond , Paul Milewski , Dimitrios Mitsotakis

In this work, a new compact sixth order accurate finite difference scheme for the two and three-dimensional Helmholtz equation is presented. The main significance of the proposed scheme is that its sixth order leading truncation error term…

Numerical Analysis · Mathematics 2024-09-23 Neelesh Kumar , Ritesh Kumar Dubey

We present a robust and efficient target-based mesh adaptation methodology, building on hybridized discontinuous Galerkin schemes for (nonlinear) convection-diffusion problems, including the compressible Euler and Navier-Stokes equations.…

Numerical Analysis · Mathematics 2014-11-12 Michael Woopen , Georg May , Jochen Schütz

An error estimate for a canonical discretization of the harmonic map heat flow into spheres is derived. The numerical scheme uses standard finite elements with a nodal treatment of linearized unit-length constraints. The analysis is based…

Numerical Analysis · Mathematics 2022-08-18 Sören Bartels , Balázs Kovács , Zhangxian Wang

An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages…