Related papers: Convergence of infinite element methods for scalar…
We develop an essentially optimal numerical method for solving multiscale Maxwell wave equations in a domain $D\subset{\mathbb R}^d$. The problems depend on $n+1$ scales: one macroscopic scale and $n$ microscopic scales. Solving the…
We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…
To model the propagation of large water waves and associated loads applied to offshore structures, scientists and engineers have a need of fast and accurate models. A wide range of models have been developped in order to predict wave-fields…
The present paper proposes and analyzes an interior penalty technique using $C^0$-finite elements to solve the Maxwell equations in domains with heterogeneous properties. The convergence analysis for the boundary value problem and the…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
On Bakhvalov-type mesh, uniform convergence analysis of finite element method for a 2-D singularly perturbed convection-diffusion problem with exponential layers is still an open problem. Previous attempts have been unsuccessful. The…
We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
The numerical analysis of elastic wave propagation in unbounded media may be difficult to handle due to spurious waves reflected at the model artificial boundaries. Several sophisticated techniques such as nonreflecting boundary conditions,…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…
One of the reasons for the success of the finite element method is its versatility to deal with different types of geometries. This is particularly true of problems posed in curved domains of arbitrary shape. In the case of second order…
The aim of this paper is to establish convergence, properties and error bounds for the fully discrete solutions of a class of nonlinear systems of reaction-diffusion nonlocal type with moving boundaries, using the finite element method with…
This paper is devoted to the study of a novel mixed Finite Element Method for approximating the solutions of fourth order variational problems subjected to a constraint. The first problem we consider consists in establishing the convergence…
In this paper, the linear finite element method on a Bakhvalov-type mesh is applied to a singularly perturbed problem with two parameters. The solution of the problem exists two exponential boundary layers. A new interpolation, which is…
The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamental solution. A theoretical framework for the convergence…
This paper analyzes the nonlinear correspondence between the reflectivity profile (model) and the plane wave impulse response at the boundary (data) for a three-dimensional half space consisting of a sequence of homogeneous horizontal…
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…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
We define a new finite element method for a steady state elliptic problem with discontinuous diffusion coefficients where the meshes are not aligned with the interface. We prove optimal error estimates in the $L^2$ norm and $H^1$ weighted…