Related papers: A Penalty-Free Asymmetric Nitsche's Method for Edg…
This article addresses the solvability of the multi-dimensional divergence-curl problem with a no-slip boundary condition. A solvability criterion is derived as an orthogonality condition of the vorticity function to pseudo-harmonic fields.…
The Boundary Element Method (BEM) is implemented using piecewise linear elements to solve the two-dimensional Dirichlet problem for Laplace's equation posed on a disk. A benefit of the BEM as opposed to many other numerical solution…
We present a new discretization method for homogeneous convection-diffusion-reaction boundary value problems in 3D that is a non-standard finite element method with PDE-harmonic shape functions on polyhedral elements. The element stiffness…
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…
We investigate error bounds for numerical solutions of divergence structure linear elliptic PDEs on compact manifolds without boundary. Our focus is on a class of monotone finite difference approximations, which provide a strong form of…
We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element…
We modify a three-field formulation of the Poisson problem with Nitsche approach for approximating Dirichlet boundary conditions. Nitsche approach allows us to weakly impose Dirichlet boundary condition but still preserves the optimal…
This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries. These IFE methods…
We study the asymptotic Dirichlet problem for the minimal graph equation on a Cartan-Hadamard manifold $M$ whose radial sectional curvatures outside a compact set satisfy an upper bound $$K(P)\le - \frac{\phi(\phi-1)}{r(x)^2}$$ and a…
Consider the scattering of an elastic plane wave by a rigid obstacle, which is immersed in a homogeneous and isotropic elastic medium in two dimensions. Based on a Dirichlet-to-Neumann (DtN) operator, an exact transparent boundary condition…
This article examines the Dirichlet boundary control problem governed by the Poisson equation, where the control variables are square integrable functions defined on the boundary of a two dimensional bounded, convex, polygonal domain. It…
We present and analyze a linearized finite element method (FEM) for the dynamical incompressible magnetohydrodynamics (MHD) equations. The finite element approximation is based on mixed conforming elements, where Taylor--Hood type elements…
We introduce a penalty term-based splitting algorithm with inertial effects designed for solving monotone inclusion problems involving the sum of maximally monotone operators and the convex normal cone to the (nonempty) set of zeros of a…
In this paper, we propose the unfitted spectral element method for solving elliptic interface and corresponding eigenvalue problems. The novelty of the proposed method lies in its combination of the spectral accuracy of the spectral element…
We develop an efficient reduced basis method for the frictional contact problem formulated using Nitsche's method. We focus on the regime of small deformations and on Tresca friction. The key idea ensuring the computational efficiency of…
We construct and analyze a TraceFEM discretization for the surface biharmonic problem. The method utilizes standard quadratic Lagrange finite element spaces defined on a three-dimensional background mesh and a symmetric $C^0$ interior…
Stable and accurate modeling of thin shells requires proper enforcement of all types of boundary conditions. Unfortunately, for Kirchhoff-Love shells, strong enforcement of Dirichlet boundary conditions is difficult because both functional…
In this paper, we develop two fully nonconforming (both H(grad curl)-nonconforming and H(curl)-nonconforming) finite elements on cubical meshes which can fit into the Stokes complex. The newly proposed elements have 24 and 36 degrees of…
A Finite Element procedure based on a full implicit backward Euler predictor/corrector scheme for the Cosserat continuum is here presented. Since this is based on invariants of the stress and couple stress tensors and on the spectral…
We consider a system of second order non-linear elliptic partial differential equations that models the equilibrium configurations of a two dimensional planar bistable nematic liquid crystal device. Discontinuous Galerkin finite element…