相关论文: Numerical approximation of the singularly perturbe…
An initial-boundary value problem for the time-fractional diffusion equation is discretized in space using continuous piecewise-linear finite elements on a polygonal domain with a re-entrant corner. Known error bounds for the case of a…
We study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle $ \Omega \subset \mathbb{R}^3 $. From the Stratton-Chu integral representation, we derive a new representation formula when constant…
A singularly perturbed convection-diffusion problem,posed on the unit square in $\mathbb{R}^2$, is studied; its solution has both exponential and characteristic boundary layers. The problem is solved numerically using the local…
We present recent finite element numerical results on a model convection-diffusion problem in the singular perturbed case when the convection term dominates the problem. We compare the standard Galerkin discretization using the linear…
In this paper, a boundary value problem for a singularly perturbed linear system of two second order ordinary differential equations of convection- diffusion type is considered on the interval [0, 1]. The components of the solution of this…
This paper is concerned with the design of two different classes of Galerkin boundary element methods for the solution of high-frequency sound-hard scattering problems in the exterior of two-dimensional smooth convex scatterers. Both…
We propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modelling magnetic plasma equilibrium in axisymmetric confinement devices. In the fixed boundary case, the equation is posed on curved…
We show that a certain error estimate for a fully discrete finite element approximation of the solution of the heat equation which is defined in a two-dimensional Euclidean domain carries over to the case of a general linear parabolic…
We consider the space-time boundary element method (BEM) for the heat equation with prescribed initial and Dirichlet data. We propose a residual-type a posteriori error estimator that is a lower bound and, up to weighted $L_2$-norms of the…
A singularly perturbed convection-diffusion problem posed on the unit square in $\mathbb{R}^2$, whose solution has exponential boundary layers, is solved numerically using the local discontinuous Galerkin (LDG) method with piecewise…
In this paper, we consider the extension of the finite element exterior calculus from elliptic problems, in which the Hodge Laplacian is an appropriate model problem, to parabolic problems, for which we take the Hodge heat equation as our…
We present and analyze a methodology for numerical homogenization of spatial networks, modelling e.g. diffusion processes and deformation of mechanical structures. The aim is to construct an accurate coarse model of the network. By solving…
In this note we describe a space-time boundary element discretization of the heat equation and an efficient and robust preconditioning strategy which is based on the use of boundary integral operators of opposite orders, but which requires…
We study a time fractional heat equation in a noncylindrical domain. The problem is one-dimensional. We prove existence of properly defined weak solutions by means of the Galerkin approximation.
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
We propose and analyze a space-time Local Discontinuous Galerkin method for the approximation of the solution to parabolic problems. The method allows for very general discrete spaces and prismatic space-time meshes. Existence and…
We consider a model convection-diffusion problem and present our recent numerical and analysis results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the…
We consider an initial and Dirichlet boundary value problem for a semilinear, two dimensional heat equation over a rectangular domain. The problem is discretized in time by a version of the Relaxation Scheme proposed by C. Besse (C. R.…
We present a novel discontinuous Galerkin finite element method for numerical simulations of the rotating thermal shallow water equations in complex geometries using curvilinear meshes, with arbitrary accuracy. We derive an entropy…
In Lipschitz domains, we study a Darcy-Forchheimer problem coupled with a singular heat equation by a nonlinear forcing term depending on the temperature. By singular we mean that the heat source corresponds to a Dirac measure. We establish…