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We present the construction and application of a first order stabilization-free virtual element method to problems in plane elasticity. Well-posedness and error estimates of the discrete problem are established. The method is assessed on a…

Numerical Analysis · Mathematics 2023-03-17 Alvin Chen , N. Sukumar

We design a primal-dual stabilized finite element method for the numerical approximation of a data assimilation problem subject to the acoustic wave equation. For the forward problem, piecewise affine, continuous, finite element functions…

Numerical Analysis · Mathematics 2023-05-10 Erik Burman , Ali Feizmohammadi , Lauri Oksanen

We present a new hyperviscosity formulation for stabilizing radial basis function-finite difference (RBF-FD) discretizations of advection-diffusion-reaction equations on manifolds $\mathbb{M} \subset \mathbb{R}^3$ of co-dimension one. Our…

Numerical Analysis · Mathematics 2020-04-27 Varun Shankar , Grady B. Wright , Akil Narayan

One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations, is to render them from their hyperbolic character to elliptic form. This paper is devoted to the study of the stabilized linear…

Numerical Analysis · Mathematics 2024-09-23 M. Asadzadeh , L. Beilina

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…

Numerical Analysis · Mathematics 2016-09-23 Lorenz Berger , Rafel Bordas , David Kay , Simon Tavener

We consider a finite element method with symmetric stabilisation for the discretisation of the transient convection--diffusion equation. For the time-discretisation we consider either the second order backwards differentiation formula or…

Numerical Analysis · Mathematics 2020-12-11 Erik Burman , Johnny Guzman

We present a numerical investigation of residual-based a posteriori error estimation for finite element discretizations of convection--diffusion equations stabilized by algebraic flux correction and related algebraic stabilization…

Numerical Analysis · Mathematics 2026-02-17 Naveed Ahmed , Abhinav Jha

In this paper we formulate and analyse adaptive (space-time) least-squares finite element methods for the solution of convection-diffusion equations. The convective derivative $\mathbf{v} \cdot \nabla u$ is considered as part of the total…

Numerical Analysis · Mathematics 2025-09-16 Christian Köthe , Olaf Steinbach

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…

Numerical Analysis · Mathematics 2024-08-21 Timo Heister , Maxim A. Olshanskii , Vladimir Yushutin

We analyze an advection-diffusion-reaction problem with non-homogeneous boundary conditions that models the chromatography process, a vital stage in bioseparation. We prove stability and error estimates for both constant and affine…

Numerical Analysis · Mathematics 2025-10-28 Farjana Siddiqua , Catalin Trenchea

In this work, we derive a reliable and efficient residual-typed error estimator for the finite element approximation of a 2d cathodic protection problem governed by a steady-state diffusion equation with a nonlinear boundary condition. We…

Numerical Analysis · Mathematics 2019-08-21 Guanglian Li , Yifeng Xu

In this paper we establish a stability barrier of a class of high-order Hermite-type discretization of 1D advection equations underlying the hybrid-variable (HV) and active flux (AF) methods. These methods seek numerical approximations to…

Numerical Analysis · Mathematics 2025-05-12 Xianyi Zeng

In this work, we consider an extension to parabolic problems of the variational multiscale method with spectral approximation of the sub-scales. We first discretize in time using a finite difference scheme and second, apply the…

Numerical Analysis · Mathematics 2018-01-25 Tomás Chacón Rebollo , Soledad Fernández-García

We consider a second order singularly perturbed boundary value problem, of reaction-convection-diffusion type with two small parameters, and the approximation of its solution by the $hp$ version of the Finite Element Method on the so-called…

Numerical Analysis · Mathematics 2020-04-20 Irene Sykopetritou , Christos Xenophontos

In this paper, we propose and analyze a numerically stable and convergent scheme for a convection-diffusion-reaction equation in the convection-dominated regime. Discontinuous Galerkin (DG) methods are considered since standard finite…

Numerical Analysis · Mathematics 2024-04-10 Satyajith Bommana Boyana , Thomas Lewis , Sijing Liu , Yi Zhang

Our aim is to study the backward problem, i.e. recover the initial data from the terminal observation, of the subdiffusion with time dependent coefficients. First of all, by using the smoothing property of solution operators and a…

Numerical Analysis · Mathematics 2023-02-01 Zhengqi Zhang , Zhi Zhou

In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the interface align with the triangulation. The velocity solution and pressure…

Numerical Analysis · Mathematics 2021-01-19 Xiaoxiao He , Fei Song , Weibing Deng

We present goal-oriented a posteriori error estimates for the automatic variationally stable finite element (AVS FE) method for scalar-valued convection-diffusion problems. The AVS-FE method is a Petrov-Galerkin method in which the test…

Numerical Analysis · Mathematics 2021-05-12 Eirik Valseth , Albert Romkes

In this paper we consider stabilised finite element methods for hyperbolic transport equations without coercivity. Abstract conditions for the convergence of the methods are introduced and these conditions are shown to hold for three…

Numerical Analysis · Mathematics 2014-05-05 Erik Burman

This paper presents a novel method for solving the 2D advection-diffusion equation using fixed-depth symbolic regression and symbolic differentiation without expression trees. The method is applied to two cases with distinct initial and…

Computation · Statistics 2024-11-12 Edward Finkelstein