Sep 2026· Proceedings in Applied Mathematics and Mechanics· Vol 26· 0 citations· 9 references
Abstract
We present a numerical study of a weakly symmetric dual‐mixed finite element method for the Stokes source problem, in which the Cauchy stress is the primary unknown and its symmetry is imposed weakly through a vorticity Lagrange multiplier. Viewing the scheme as the incompressible limit of the reduced‐symmetry mixed elasticity framework, we employ the Raviart–Thomas based family , which approximates stress, velocity and vorticity to the uniform order . We recall the corresponding a priori error estimates and a local velocity postprocessing that superconverges with order , and we describe the hybridisation and element‐wise static condensation that the balanced family admits, which retains a single piecewise‐constant pressure unknown per element and reduces the globally coupled system to between roughly and of its full size in both two and three dimensions. All estimates are illustrated by numerical experiments on the unit square and the unit cube. The formulation also provides the basis for the stress‐based Stokes eigenvalue problem we treat in forthcoming work.
We develop and analyze a structure-preserving discretization for the coupled Stokes–Biot equations. The method is based on a fully-mixed formulation and computes directly the fluid and poroelastic stresses and the Darcy velocity. The scheme employs equal-order polynomial approximations for all unknowns, yet exhibits lo...
I. Yotov, L. Zhao· ESAIM: Mathematical Modellin...· 0 citations
In this paper we propose augmented Lagrangian finite element methods for cavitation in the Reynolds and Stokes models of lubrication, for which the discrete complementarity conditions hold exactly and the augmentation parameter drops out of the method. For the Reynolds equation this follows from nodal quadrature in a m...
We propose and analyze new mixed finite element methods for the linear poroelasticity problem,
which models the coupled phenomena of fluid diffusion and solid deformation. The formulation
is based on the introduction of the vorticity and the strain tensor as auxiliary unknowns, which makes it possible
to eliminate t...
Alonso J. Bustos, G. Gatica, R. Ruiz-Baier et al.· ESAIM: Mathematical Modellin...· 0 citations
We develop and analyze a fully discrete finite difference approximation for a damped shear beam model with mixed boundary conditions and no rotational inertia. The absence of a second‐order time derivative in the rotational equation gives rise to an asymmetric temporal structure. This structural feature motivates a d...
Anderson de Jesus Araújo Ramos, André Fellipe Ribeiro de Almeida, M. D. Dos Santos et al.· Mathematical methods in the...· 0 citations
We study the two-dimensional compressible Navier-Stokes-Poisson system in a general simply connected bounded domain with Navier-slip boundary conditions and a positive, possibly non-flat, doping profile. We establish the global existence of a unique strong solution and of a global weak solution for arbitrarily large in...
Ying-Zhi Du, Hui-Jiang Zhao· 0 citations
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