Related papers: Optimal $L^2$-error estimates for the nonsymmetric…

We propose two different discrete formulations for the weak imposition of the Neumann boundary conditions of the Darcy flow. The Raviart-Thomas mixed finite element on both triangular and quadrilateral meshes is considered for both methods.…

A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…

We construct and analyse a $hp$-FE/BE coupling on non-matching meshes, based on Nitsche's method. Both the mesh size and the polynomial degree are changed to improve accuracy. Nitsche's method leads to a positive definite formulation, thus,…

In two-dimensional Lipschitz domains, we analyze a Brinkman--Darcy--Forchheimer problem on the weighted spaces $\mathbf{H}_0^1(\omega,\Omega) \times L^2(\omega,\Omega)/\mathbb{R}$, where $\omega$ belongs to the Muckenhoupt class $A_2$.…

We prove that the solutions to the discrete Nonlinear Schr\"odinger Equation (DNLSE) with non-local algebraically-decaying coupling converge strongly in $L^2(\mathbb{R}^2)$ to those of the continuum fractional Nonlinear Schr\"odinger…

Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…

This work proposes and analyzes a fully discrete numerical scheme for solving the Landau-Lifshitz-Gilbert (LLG) equation, which achieves fourth-order spatial accuracy and third-order temporal accuracy.Spatially, fourth-order accuracy is…

In this paper, the author derives an $O(h^4)$-superconvergence for the piecewise linear Ritz-Galerkin finite element approximations for the second order elliptic equation $-\nabla \cdot(A\nabla u)= f$ equipped with Dirichlet boundary…

We consider the stochastic Cahn-Hilliard equation driven by additive Gaussian noise in a convex domain with polygonal boundary in dimension $d\le 3$. We discretize the equation using a standard finite element method in space and a fully…

The biharmonic equation with Dirichlet and Neumann boundary conditions discretized using the mixed finite element method and piecewise linear (with the possible exception of boundary triangles) finite elements on triangular elements has…

We establish uniform Lipschitz estimates for second-order elliptic systems in divergence form with rapidly oscillating, almost-periodic coefficients. We give interior estimates as well as estimates up to the boundary in bounded…

This paper establishes an explicit $L^2$-estimate for weak solutions $u$ to linear elliptic equations in divergence form with general coefficients and external source term $f$, stating that the $L^2$-norm of $u$ over $U$ is bounded by a…

In this paper, we develop a new multiphysics finite element method for a nonlinear poroelastic model with Hencky-Mises stress tensor. By introducing some new notations, we reformulate the original model into a fluid-fluid coupling problem,…

We prove an optimal error estimate for the flux variable for a stabilized unfitted Nitsche finite element method applied to an elliptic interface problem with discontinuous constant coefficients. Our result shows explicitly that this error…

In this note we design a cut finite element method for a low order divergence free element applied to a boundary value problem subject to Stokes' equations. For the imposition of Dirichlet boundary conditions we consider either Nitsche's…

We construct and analyze finite element approximations of the Einstein tensor in dimension $N \ge 3$. We focus on the setting where a smooth Riemannian metric tensor $g$ on a polyhedral domain $\Omega \subset \mathbb{R}^N$ has been…

We extend a distributed finite element method built upon model order reduction to arbitrary polynomial degree using a hybrid Nitsche scheme. The new method considerably simplifies the transformation of the finite element system to the…

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of…

In this article we develop convergence theory for a class of goal-oriented adaptive finite element algorithms for second order nonsymmetric linear elliptic equations. In particular, we establish contraction results for a method of this type…

We study finite element approximations of the nonhomogeneous Dirichlet problem for the fractional Laplacian. Our approach is based on weak imposition of the Dirichlet condition and incorporating a nonlocal analogous of the normal derivative…