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Numerical approximation of a stochastic partial integro-differential equation driven by a space- time white noise is studied by truncating a series representation of the noise, with finite element method for spatial discretization and…

Numerical Analysis · Mathematics 2017-11-07 Max Gunzburger , Buyang Li , Jilu Wang

We derive and analyze a broad class of finite element methods for numerically simulating the stationary, low Reynolds number flow of concentrated mixtures of several distinct chemical species in a common thermodynamic phase. The underlying…

Numerical Analysis · Mathematics 2025-09-24 Aaron Baier-Reinio , Patrick E. Farrell

This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…

Computational Engineering, Finance, and Science · Computer Science 2023-05-23 Juan F. Giraldo , Victor M. Calo

We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…

Numerical Analysis · Mathematics 2020-03-23 Ulrich Langer , Andreas Schafelner

We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear…

Numerical Analysis · Mathematics 2016-02-09 Yana Di , Hehu Xie , Xiaobo Yin

In this work we study various continuous finite element discretization for two dimensional hyperbolic partial differential equations, varying the polynomial space (Lagrangian on equispaced, Lagrangian on quadrature points (Cubature) and…

Numerical Analysis · Mathematics 2023-06-16 Sixtine Michel , Davide Torlo , Mario Ricchiuto , Rémi Abgrall

Locally refined meshes impose severe stability constraints on explicit time-stepping methods for the numerical simulation of time dependent wave phenomena. Local time-stepping methods overcome that bottleneck by using smaller time-steps…

Numerical Analysis · Mathematics 2012-10-19 Marcus Grote , Teodora Mitkova

In this paper we study semi-discrete and fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation with a logarithmic potential. Specifically we consider linear finite elements discretising space and backward…

Numerical Analysis · Mathematics 2025-09-11 Charles M. Elliott , Thomas Sales

We study a higher-order surface finite element (SFEM) penalty-based discretization of the tangential surface Stokes problem. Several discrete formulations are investigated which are equivalent in the continuous setting. The impact of the…

Numerical Analysis · Mathematics 2025-03-11 Hanne Hardering , Simon Praetorius

In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous…

Numerical Analysis · Mathematics 2016-05-25 Peter Hansbo , Mats G. Larson , Sara Zahedi

In this paper, we develop regularized discrete least squares collocation and finite volume methods for solving two-dimensional nonlinear time-dependent partial differential equations on irregular domains. The solution is approximated using…

Numerical Analysis · Mathematics 2019-06-26 Fanhai Zeng , Ian Turner , Kevin Burrage , Stephen J. Wright

In this paper we study finite element method for three-dimensional incompressible resistive magnetohydrodynamic equations, in which the velocity, the current density, and the magnetic induction are divergence-free. It is desirable that the…

Numerical Analysis · Mathematics 2021-02-03 Lingxiao Li , Donghang Zhang , Weiying Zheng

The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in three-dimensional space. The method employs generalized Taylor-Hood finite element pairs on tetrahedral bulk mesh to discretize the…

Numerical Analysis · Mathematics 2020-03-17 Thomas Jankuhn , Maxim A. Olshanskii , Arnold Reusken , Alexander Zhiliakov

In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…

We design an adaptive unfitted finite element method on the Cartesian mesh with hanging nodes. We derive an hp-reliable and efficient residual type a posteriori error estimate on K-meshes. A key ingredient is a novel hp-domain inverse…

Numerical Analysis · Mathematics 2021-10-12 Zhiming Chen , Ke Li , Xueshuang Xiang

It is significant and challenging to solve eigenvalue problems of partial differential operators when many highly accurate eigenpair approximations are required. The adaptive finite element discretization based parallel orbital-updating…

Numerical Analysis · Mathematics 2025-09-24 Xiaoying Dai , Yan Li , Bin Yang , Aihui Zhou

A moving mesh finite difference method based on the moving mesh partial differential equation is proposed for the numerical solution of the 2T model for multi-material, non-equilibrium radiation diffusion equations. The model involves…

Numerical Analysis · Mathematics 2020-04-20 Xiaobo Yang , Weizhang Huang , Jianxian Qiu

This paper establishes a continuous time approximation, a piece-wise continuous differential equation, for the discrete Heavy-Ball (HB) momentum method with explicit discretization error. Investigating continuous differential equations has…

Machine Learning · Computer Science 2025-10-23 Bochen Lyu , Xiaojing Zhang , Fangyi Zheng , He Wang , Zheng Wang , Zhanxing Zhu

Fractional order models have proven to be a very useful tool for the modeling of the mechanical behaviour of viscoelastic materials. Traditional numerical solution methods exhibit various undesired properties due to the non-locality of the…

Numerical Analysis · Mathematics 2023-01-30 Kai Diethelm

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method…

Numerical Analysis · Mathematics 2017-09-01 Christoph Lehrenfeld , Arnold Reusken