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We study a numerical method for convection diffusion equations, in the regime of small viscosity. It can be described as an exponentially fitted conforming Petrov-Galerkin method. We identify norms for which we have both continuity and an…
Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in…
We present a new analytical and numerical framework for solution of Partial Differential Equations (PDEs) that is based on an exact transformation that moves the boundary constraints into the dynamics of the corresponding governing…
In this paper we formulate a transmission problem for the transient acoustic wave equation as a system of retarded boundary integral equations. We then analyse a fully discrete method using a general Galerkin semidiscretization-in-space and…
We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model…
This paper presents the first analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains. The analysis is based on non-standard local trace and inverse inequalities…
We consider the discretization of electromagnetic wave propagation problems by a discontinuous Galerkin Method based on Trefftz polynomials. This method fits into an abstract framework for space-time discontinuous Galerkin methods for which…
We propose a reformulation of the boundary integral equations for the Helmholtz equation in a domain in terms of incoming and outgoing boundary waves. We obtain transfer operator descriptions which are exact and thus incorporate features…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
The convergence rate of domain decomposition methods (DDMs) strongly depends on the transmission condition at the interfaces between subdomains. Thus, an important aspect in improving the efficiency of such solvers is careful design of…
In this paper we present a novel approach for the design of high order general boundary conditions when approximating solutions of the Euler equations on domains with curved boundaries, using meshes which may not be boundary conformal. When…
We propose a time stepping scheme for the space-time systems obtained from Galerkin time-domain boundary element methods for the wave equation. Based on extrapolation, the method proves stable, becomes exact for increasing degrees of…
Inferring electromagnetic propagation characteristics within the marine atmospheric boundary layer (MABL) from data in real time is crucial for modern maritime navigation and communications. The propagation of electromagnetic waves is well…
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial…
We consider second-order PDE problems set in unbounded domains and discretized by Lagrange finite elements on a finite mesh, thus introducing an artificial boundary in the discretization. Specifically, we consider the reaction diffusion…
It is well known that the Fourier series Dirichlet-to-Neumann (DtN) boundary condition can be used to solve the Helmholtz equation in unbounded domains. In this work, applying such DtN boundary condition and using the finite element method,…
The propagation of electromagnetic waves in a linearly-varying index of refraction is a fundamental problem in wave physics, being relevant in fusion science for describing certain wave-based heating and diagnostic schemes. Here, an exact…
We deal with non-hydrostatic mesoscale atmospheric modeling using the fully implicit space-time discontinuous Galerkin method in combination with the anisotropic $hp$-mesh adaptation technique. The time discontinuous approximation allows…
Translations or, more generally, coordinate transformations of scalar fields arise in several applications, such as weather, accretion disk and magnetized plasma turbulence modeling. In local studies of accretion disks and magnetized…
In this article, we propose novel boundary treatment algorithms to avoid order reduction when implicit-explicit Runge-Kutta time discretization is used for solving convection-diffusion-reaction problems with time-dependent Di\-richlet…