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The paper addresses stability and finite element analysis of the stationary two-phase Stokes problem with a piecewise constant viscosity coefficient experiencing a jump across the interface between two fluid phases. We first prove a priori…

Numerical Analysis · Mathematics 2020-04-23 Ernesto Cáceres , Johnny Guzmán , Maxim Olshanskii

In this paper, new unfitted mixed finite elements are presented for elliptic interface problems with jump coefficients. Our model is based on a fictitious domain formulation with distributed Lagrange multiplier. The relevance of our…

Numerical Analysis · Mathematics 2023-09-15 Najwa Alshehri , Daniele Boffi , Lucia Gastaldi

In this article, we aim to recover locally conservative and $H(div)$ conforming fluxes for the linear Cut Finite Element Solution with Nitsche's method for Poisson problems with Dirichlet boundary condition. The computation of the…

Numerical Analysis · Mathematics 2021-06-07 Daniela Capatina , Cuiyu He

We propose and analyze an unfitted finite element method for solving elliptic problems on domains with curved boundaries and interfaces. The approximation space on the whole domain is obtained by the direct extension of the finite element…

Numerical Analysis · Mathematics 2021-12-28 Fanyi Yang , Xiaoping Xie

In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media whose permeability and porosity are discontinuous across some…

Numerical Analysis · Mathematics 2014-06-18 Buyang Li , Hongxing Rui , Chaoxia Yang

A low diffusive flux difference splitting based kinetic scheme is developed based on a discrete velocity Boltzmann equation, with a novel three velocity model. While two discrete velocities are used for upwinding, the third discrete…

Fluid Dynamics · Physics 2024-10-01 Shrinath. K. S , Maruthi. N. H , S. V. Raghurama Rao , Veeredhi Vasudeva Rao

We introduce a flux recovery scheme for the computed solution of a quadratic immersed finite element method. The recovery is done at nodes and interface point first and by interpolation at the remaining points. We show that the end nodes…

Numerical Analysis · Mathematics 2015-12-16 So-Hsiang Chou , C. Attanayake

In this paper we introduce and analyze the residual-based a posteriori error estimation of the partially penalized immersed finite element method for solving elliptic interface problems. The immersed finite element method can be naturally…

Numerical Analysis · Mathematics 2019-10-18 Cuiyu He , Xu Zhang

We show quasi-optimality and a posteriori error estimates for the frictionless contact problem between two elastic bodies with a zero-gap function. The analysis is based on interpreting Nitsche's method as a stabilised finite element method…

Numerical Analysis · Mathematics 2020-03-05 Tom Gustafsson , Rolf Stenberg , Juha Videman

We formulate and analyze a Nitsche-type algorithm for frictional contact problems. The method is derived from, and analyzed as, a stabilized finite element method and shown to be quasi-optimal, as well as suitable as an adaptive scheme…

Numerical Analysis · Mathematics 2021-06-24 Tom Gustafsson , Juha Videman

In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…

Numerical Analysis · Mathematics 2013-08-05 Erik Burman

For elliptic interface problems in two- and three-dimensions with a possible very low regularity, this paper establishes a priori error estimates for the Raviart-Thomas and Brezzi-Douglas-Marini mixed finite element approximations. These…

Numerical Analysis · Mathematics 2019-03-01 Shun Zhang

Motivated by the study of the electrodynamics of particles, we propose in this work an arbitrary-order discrete de Rham scheme for the treatment of elliptic problems with potential and flux jumps across a fixed interface. The scheme…

Numerical Analysis · Mathematics 2024-09-24 Daniele A. Di Pietro , Simon Mendez , Aurelio Edoardo Spadotto

We propose a low-dimensional interface reduction method for elliptic interface problems based on conservative flux reconstruction. The approach combines a fitted $P_1$ finite element discretization with a flux recovery procedure following…

Numerical Analysis · Mathematics 2026-05-12 C. Attanayake , So-Hsiang Chou

We consider energy norm a posteriori error analysis of conforming finite element approximations of singularly perturbed reaction-diffusion problems on simplicial meshes in arbitrary space dimension. Using an equilibrated flux…

Numerical Analysis · Mathematics 2020-11-25 Iain Smears , Martin Vohralík

In this note we show that the non-symmetric version of the classical Nitsche's method for the weak imposition of boundary conditions is stable without penalty term. We prove optimal $H^1$-error estimates and $L^2$-estimates that are…

Numerical Analysis · Mathematics 2011-11-07 Erik Burman

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

Robust mixed finite element methods are developed for a quad-curl singular perturbation problem. Lower order H(grad curl)-nonconforming but H(curl)-conforming finite elements are constructed, which are extended to nonconforming finite…

Numerical Analysis · Mathematics 2022-06-24 Xuehai Huang , Chao Zhang

We introduce an unfitted Nitsche finite element method with a new ghost-penalty stabilization based on local projection of the solution gradient. The proposed ghost-penalty operator is straightforward to implement, ensures algebraic…

Numerical Analysis · Mathematics 2025-09-03 Maxim Olshanskii , Jan-Phillip Bäcker , Dmitri Kuzmin

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