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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 an arbitrary order discontinuous Galerkin finite element method for solving the biharmonic interface problem on the unfitted mesh. The approximation space is constructed by a patch reconstruction process with at most one degree…

Numerical Analysis · Mathematics 2023-05-08 Yan Chen , Ruo Li , Qicheng Liu

We propose two classes of mixed finite elements for linear elasticity of any order, with interior penalty for nonconforming symmetric stress approximation. One key point of our method is to introduce some appropriate nonconforming…

Numerical Analysis · Mathematics 2017-05-22 Shuonan Wu , Shihua Gong , Jinchao Xu

This paper develops and analyzes an interior penalty discontinuous Galerkin (IPDG) method using piecewise linear polynomials for the indefinite time harmonic Maxwell equations with the impedance boundary condition in the three dimensional…

Numerical Analysis · Mathematics 2012-12-11 Xiaobing Feng , Haijun Wu

Unfitted finite element techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to severe ill conditioning problems that obstruct the efficient use…

Computational Engineering, Finance, and Science · Computer Science 2018-05-09 Santiago Badia , Francesc Verdugo , Alberto F. Martín

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 work, we consider an initial-boundary value problem for a time-fractional biharmonic equation in a bounded polygonal domain with a Lipschitz continuous boundary in $\mathbb{R}^2$ with clamped boundary conditions. After establishing…

Numerical Analysis · Mathematics 2024-07-29 Shantiram Mahata , Neela Nataraj , Jean-Pierre Raymond

We demonstrate the ability of a stabilized finite element method, inspired by the weighted Nitsche approach, to alleviate spurious traction oscillations at interlaminar interfaces in multi-ply multi-directional composite laminates. In…

Computational Engineering, Finance, and Science · Computer Science 2020-08-21 Gourab Ghosh , Ravindra Duddu , Chandrasekhar Annavarapu

We develop the max-plus finite element method to solve finite horizon deterministic optimal control problems. This method, that we introduced in a previous work, relies on a max-plus variational formulation, and exploits the properties of…

Optimization and Control · Mathematics 2016-11-18 Marianne Akian , Stephane Gaubert , Asma Lakhoua

We investigate the numerical approximation of an elliptic optimal control problem which involves a nonconvex local regularization of the $L^q$-quasinorm penalization (with $q\in(0,1)$) in the cost function. Our approach is based on the…

Optimization and Control · Mathematics 2022-09-26 Pedro Merino , Alexander Nenjer

This paper is concerned with a numerical solution to the scattering of a time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in three dimensions. The electromagnetic wave propagation is modeled by a boundary value…

Numerical Analysis · Mathematics 2022-02-21 Gang Bao , Mingming Zhang , Xue Jiang , Peijun Li , Xiaokai Yuan

We use inverted finite elements method for approximating solutions of second order elliptic equations with non-constant coefficients varying to infinity in the exterior of a 2D bounded obstacle, when a Neumann boundary condition is…

Numerical Analysis · Mathematics 2025-01-24 R Belbaki , S K Bhowmik , T Z Boulmezaoud , N Kerdid , S Mziou

We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$…

Numerical Analysis · Mathematics 2019-02-05 Erik Burman , Peter Hansbo , Mats G. Larson , Karl Larsson

In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…

Numerical Analysis · Mathematics 2014-03-21 Klaus Deckelnick , Charles M. Elliott , Thomas Ranner

Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…

Numerical Analysis · Mathematics 2025-06-24 Robert C. Kirby , John D. Stephens

The isogeometric approximation of the Stokes problem in a trimmed domain is studied. This setting is characterized by an underlying mesh unfitted with the boundary of the physical domain making the imposition of the essential boundary…

Numerical Analysis · Mathematics 2022-02-02 Riccardo Puppi

Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…

Numerical Analysis · Mathematics 2022-10-13 Patrick E. Farrell , Abdalaziz Hamdan , Scott P. MacLachlan

We introduce and analyze a robust nonconforming finite element method for a three dimensional singularly perturbed quad-curl model problem. For the solution of the model problem, we derive proper a priori bounds, based on which, we prove…

Numerical Analysis · Mathematics 2022-06-27 Baiju Zhang , Zhimin Zhang

We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…

Optimization and Control · Mathematics 2019-09-23 Fei Li , Zheng Qu

This paper investigates energy-minimization finite-element approaches for the computation of nematic liquid crystal equilibrium configurations. We compare the performance of these methods when the necessary unit-length constraint is…

Numerical Analysis · Mathematics 2014-12-31 J. H. Adler , D. B. Emerson , S. P. MacLachlan , T. A. Manteuffel