Related papers: Adaptive Flux-Only Least-Squares Finite Element Me…
This paper introduces a novel adaptive framework for processing dynamic flow signals over simplicial complexes, extending classical least-mean-squares (LMS) methods to high-order topological domains. Building on discrete Hodge theory, we…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
We analyze the flux conservation property of the finite element method. It is shown that the finite element solution does approximate the flux locally in the optimal order, i.e., the same order as that of the nodal interpolation operator.…
This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique…
The paper focuses on a new error analysis of a class of mixed FEMs for stationary incompressible magnetohydrodynamics with the standard inf-sup stable velocity-pressure space pairs to Navier-Stokes equations and the N\'ed\'elec's edge…
We define and analyse a least-squares finite element method for a first-order reformulation of a scaled Brinkman model of fluid flow through porous media. We introduce a pseudostress variable that allows to eliminate the pressure variable…
In this article we present a novel staggered semi-implicit hybrid finite-volume/finite-element (FV/FE) method for the resolution of weakly compressible flows in two and three space dimensions. The pressure-based methodology introduced in…
We show that optimal $L^2$-convergence in the finite element method on quasi-uniform meshes can be achieved if, for some $s_0 > 1/2$, the boundary value problem has the mapping property $H^{-1+s} \rightarrow H^{1+s}$ for $s \in [0,s_0]$.…
The solution of computational fluid dynamics problems is one of the most computationally hard tasks, especially in the case of complex geometries and turbulent flow regimes. We propose to use Tensor Train (TT) methods, which possess…
This work focuses on a class of elliptic boundary value problems with diffusive, advective and reactive terms, motivated by the study of three-dimensional heterogeneous physical systems composed of two or more media separated by a selective…
A nonlinear Helmholtz (NLH) equation with high frequencies and corner singularities is discretized by the linear finite element method (FEM). After deriving some wave-number-explicit stability estimates and the singularity decomposition for…
We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…
A stabilized conforming mixed finite element method for the three-field (displacement, fluid flux and pressure) poroelasticity problem is developed and analyzed. We use the lowest possible approximation order, namely piecewise constant…
A nonlinear sea-ice problem is considered in a least-squares finite element setting. The corresponding variational formulation approximating simultaneously the stress tensor and the velocity is analysed. In particular, the least-squares…
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…
Achieving accurate numerical results of hydrodynamic loads based on the potential-flow theory is very challenging for structures with sharp edges, due to the singular behavior of the local-flow velocities. In this paper, we introduce the…
The time discrete scheme of characteristics type is especially effective for convection-dominated diffusion problems. The scheme has been used in various engineering areas with different approximations in spatial direction. The lowest-order…
In computational engineering, ensuring the integrity and safety of structures in fields such as aerospace and civil engineering relies on accurate stress prediction. However, analytical methods are limited to simple test cases, and…
The paper introduces an adaptive version of the stabilized Trace Finite Element Method (TraceFEM) designed to solve low-regularity elliptic problems on level-set surfaces using a shape-regular bulk mesh in the embedding space. Two…
In this article, we present a cut finite element method for two-phase Navier-Stokes flows. The main feature of the method is the formulation of a unified continuous interior penalty stabilisation approach for, on the one hand, stabilising…