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Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the…

Numerical Analysis · Mathematics 2023-05-24 Gabriel R. Barrenechea , Volker John , Petr Knobloch

The present work aims at the application of finite element discretizations to a class of equilibrium problems involving moving constraints. Therefore, a Moreau--Yosida based regularization technique, controlled by a parameter, is discussed…

Numerical Analysis · Mathematics 2021-10-07 Steven-Marian Stengl

A discretization method with non-matching grids is proposed for the coupled Stokes-Darcy problem that uses a mortar variable at the interface to couple the marker and cell (MAC) method in the Stokes domain with the Raviart-Thomas mixed…

Numerical Analysis · Mathematics 2024-02-19 Wietse M. Boon , Dennis Gläser , Rainer Helmig , Kilian Weishaupt , Ivan Yotov

We review the concept of well-posedness in the context of evolutionary problems from mathematical physics for a particular subclass of problems from elasticity theory. The complexity of physical phenomena appears as encoded in so called…

Analysis of PDEs · Mathematics 2016-10-27 Rainer Picard , Sascha Trostorff , Marcus Waurick

This paper focuses on the numerical simulation of geothermal systems in complex geological settings. The physical model is based on two-phase Darcy flows coupling the mass conservation of the water component with the energy conservation and…

We consider the systematic numerical approximation of Biot's quasistatic model for the consolidation of a poroelastic medium. Various discretization schemes have been analysed for this problem and inf-sup stable finite elements have been…

Numerical Analysis · Mathematics 2020-01-01 Herbert Egger , Mania Sabouri

This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality relations lead to simple error estimates that avoid an explicit treatment of…

Numerical Analysis · Mathematics 2020-02-07 Sören Bartels

Numerical modeling of elastic wave propagation in the subsurface requires applicability to heterogeneous, anisotropic and discontinuous media, as well as support of free surface boundary conditions. Here we study the cell-centered finite…

Numerical Analysis · Mathematics 2025-03-24 Ingrid Kristine Jacobsen , Inga Berre , Jan Martin Nordbotten , Ivar Stefansson

A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the…

Numerical Analysis · Mathematics 2019-06-27 Balázs Kovács , Buyang Li , Christian Lubich

The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general models, which are described by multifunctions between…

Optimization and Control · Mathematics 2025-04-30 Boris S. Mordukhovich , Pengcheng Wu , Xiaoqi Yang

The aim of this paper is to propose a systematic way to obtain convergent finite element schemes for the Darcy-Stokes flow problem by combining well-known mixed finite elements that are separately convergent for Darcy and Stokes problems.…

Numerical Analysis · Mathematics 2012-03-22 Antonio Márquez , Salim Meddahi , Francisco-Javier Sayas

We present recent finite element numerical results on a model convection-diffusion problem in the singular perturbed case when the convection term dominates the problem. We compare the standard Galerkin discretization using the linear…

Numerical Analysis · Mathematics 2023-02-16 Constantin Bacuta , Daniel Hayes , Tyler O'Grady

We develop and present a unified multi-scale model (involving three scales of spatial organisation) to study the dynamics of rigid aggregating particles suspended in a viscous fluid medium and subject to a steady poiseuille flow. At…

Soft Condensed Matter · Physics 2016-10-10 Sarthok Sircar , Anthony J. Roberts

In this paper we discuss the adjoint stabilised finite element method introduced in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problems. Part I: elliptic equations, SIAM Journal on Scientific…

Numerical Analysis · Mathematics 2015-12-10 Erik Burman

We introduce a topology-preserving discretization for coupling incompressible fluids with thin deformable structures, achieving guaranteed leakproofness through preservation of fluid domain connectivity. Our approach leverages a stitching…

Computational Physics · Physics 2026-02-05 Jonathan Panuelos , Eitan Grinspun , David Levin

We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…

Numerical Analysis · Mathematics 2015-03-19 Traian iliescu , Zhu Wang

In this paper, we propose a robust and efficient numerical framework for simulating multicomponent gas flow in poroelastic media, with a focus on preserving fundamental thermodynamic principles and ensuring computational reliability. The…

Numerical Analysis · Mathematics 2026-03-03 Huangxin Chen , Yuxiang Chen , Jisheng Kou , Shuyu Sun

We show that the semi-implicit time discretization approaches previously introduced for multilayer shallow water models for the barotropic case can be also applied to the variable density case with Boussinesq approximation. Furthermore,…

Numerical Analysis · Mathematics 2021-04-27 Luca Bonaventura , José Garres-Díaz

Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models…

Numerical Analysis · Mathematics 2026-04-01 Peter Gangl , Nico Nees , Michael Stingl

Two phase solid-fluid mixture models are ubiquitous in biological applications. For instance, models for growth of tissues and biofilms combine time dependent and quasi-stationary boundary value problems set in domains whose boundary moves…

Analysis of PDEs · Mathematics 2024-01-17 Ana Carpio , Gema Duro