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In this paper we present a new H(div)-conforming unfitted finite element method for the mixed Poisson problem which is robust in the cut configuration and preserves conservation properties of body-fitted finite element methods. The key is…

Numerical Analysis · Mathematics 2024-09-04 Christoph Lehrenfeld , Tim van Beeck , Igor Voulis

We propose second-order implicit-explicit (IMEX) time-stepping schemes for nonlinear fractional differential equations with fractional order $0<\beta<1$. From the known structure of the non-smooth solution and by introducing corresponding…

Numerical Analysis · Mathematics 2016-08-03 Wanrong Cao , Fanhai Zeng , Zhongqiang Zhang , George Em Karniadakis

We propose a new paradigm for designing efficient p-adaptive arbitrary high order methods. We consider arbitrary high order iterative schemes that gain one order of accuracy at each iteration and we modify them in order to match the…

Numerical Analysis · Mathematics 2023-11-09 Lorenzo Micalizzi , Davide Torlo , Walter Boscheri

In this paper we analyse full discretizations of an initial boundary value problem (IBVP) related to reaction-diffusion equations. To avoid possible order reduction, the IBVP is first transformed into an IBVP with homogeneous boundary…

Numerical Analysis · Mathematics 2021-11-18 Saint-Cyr E. R. Koyaguerebo-Imé , Yves Bourgault

We present a fully computable a posteriori error estimator for piecewise linear finite element approximations of reaction-diffusion problems with mixed boundary conditions and piecewise constant reaction coefficient formulated in arbitrary…

Numerical Analysis · Mathematics 2015-07-06 Mark Ainsworth , Tomáš Vejchodský

Implicit-Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity of interest for…

Numerical Analysis · Mathematics 2016-10-19 Jehanzeb H. Chaudhry , J. B. Collins , John N. Shadid

This paper introduces a novel approach to approximate a broad range of reaction-convection-diffusion equations using conforming finite element methods while providing a discrete solution respecting the physical bounds given by the…

Numerical Analysis · Mathematics 2023-11-28 Abdolreza Amiri , Gabriel R. Barrenechea , Tristan Pryer

Peer methods are a comprehensive class of time integrators offering numerous degrees of freedom in their coefficient matrices that can be used to ensure advantageous properties, e.g. A-stability or super-convergence. In this paper, we show…

Numerical Analysis · Mathematics 2020-10-27 Moritz Schneider , Jens Lang

We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense…

Numerical Analysis · Mathematics 2012-05-22 Lijian Jiang , Dylan Copeland , J. David Moulton

In this paper, we introduce the locally conservative enriched immersed finite element method (EIFEM) to tackle the elliptic problem with interface. The immersed finite element is useful for handling interface with mesh unfit with the…

Numerical Analysis · Mathematics 2021-01-05 Gwanghyun Jo , Do Young Kwak , Young Ju Lee

We present a one-dimensional shear-force-driven droplet formation model with a flux-based error estimator. The model is derived using asymptotic expansion and a front-tracking method to simulate the droplet interface. The model is then…

Numerical Analysis · Mathematics 2026-05-25 Darsh Nathawani , Matthew Knepley

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

Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…

Numerical Analysis · Mathematics 2023-10-03 Alan F. Hegarty , Eugene O'Riordan

Although considerable effort has been dedicated to improving the solution to the hyperspectral unmixing problem, non-idealities such as complex radiation scattering and endmember variability negatively impact the performance of most…

Image and Video Processing · Electrical Eng. & Systems 2023-10-05 Ricardo Augusto Borsoi , Deniz Erdoğmuş , Tales Imbiriba

In this paper, we propose a multiphysics finite element method for a nonlinear poroelasticity model. To better describe the processes of deformation and diffusion, we firstly reformulate the nonlinear fluid-solid coupling problem into a…

Numerical Analysis · Mathematics 2021-12-28 Zhihao Ge , Wenlong He

We present REMIX, a smoothed particle hydrodynamics (SPH) scheme designed to alleviate effects that typically suppress mixing and instability growth at density discontinuities in SPH simulations. We approach this problem by directly…

We propose a new practical adaptive refinement strategy for $hp$-finite element approximations of elliptic problems. Following recent theoretical developments in polynomial-degree-robust a posteriori error analysis, we solve two types of…

Numerical Analysis · Mathematics 2018-10-17 Patrik Daniel , Alexandre Ern , Iain Smears , Martin Vohralík

In this paper, we develop a multiphysics finite element method for solving the quasi-static thermo-poroelasticity model with nonlinear permeability. The model involves multiple physical processes such as deformation, pressure, diffusion and…

Numerical Analysis · Mathematics 2026-02-24 Zhihao Ge , Wenshuai Hu

We propose an adaptive iteratively linearized finite element method (AILFEM) in the context of strongly monotone nonlinear operators in Hilbert spaces. The approach combines adaptive mesh-refinement with an energy-contractive linearization…

Numerical Analysis · Mathematics 2025-03-18 Ani Miraçi , Dirk Praetorius , Julian Streitberger

We study the discretisation of a uniaxial (rank-one) reduction of the Oldroyd-B model for dilute polymer solutions, in which the conformation tensor is represented as $\sig = \vec b \otimes \vec b$. Building on structural analogies with…

Numerical Analysis · Mathematics 2025-11-26 Ben S. Ashby , Gabriel R. Barrenechea , Alex Lukyanov , Tristan Pryer , Alex Trenam