We propose and analyse a fully discrete Petrov–Galerkin method with quadrature, for solving second-order, variable coefficient, elliptic boundary value problems on rectangular domains. In our scheme, the trial space consists of C2 splines of degree r 3, the test space consists of C0 splines of degree r − 2, and we use composite (r − 1)-point Gauss quadrature. We show existence and uniqueness of...

In this paper we consider time-dependent electromagnetic scattering problems from conducting objects. We discretize the time-domain electric field integral equation using RungeKutta convolution quadrature in time and a Galerkin method in space. We analyze the involved operators in the Laplace domain and obtain convergence results for the fully discrete scheme. Numerical experiments indicate the...

We present a new numerical method, based on a coupling of finite elements and boundary elements, to solve a fluid–solid interaction problem posed in the plane. The boundary unknowns involved in our formulation are approximated by a spectral method. We provide error estimates for the Galerkin method, propose fully discrete schemes based on elementary quadrature formulas and show that the perturb...

We considered an hybridizable discontinuous Galerkin (HDG) method for discrete elliptic PDEs with random coefficients. By approach of projection, we obtained the error analysis under assumption that a(ω,x) is uniformly bounded. Together HDG method, applied a multilevel Monte Carlo (MLMC) (MLMC-HDG method) to simulate PDEs. derived overall convergence rate and total computation cost estimate. Fi...

We develop divergence-conforming B-spline discretizations for the numerical solution of the steady Navier-Stokes equations. These discretizations are motivated by the recent theory of isogeometric discrete differential forms and may be interpreted as smooth generalizations of Raviart-Thomas elements. They are (at least) patchwise C and can be directly utilized in the Galerkin solution of steady...

We introduce a nonoverlapping variant of the Schwarz waveform relaxation algorithm for semilinear wave propagation in one dimension. Using the theory of absorbing boundary conditions, we derive a new nonlinear algorithm. We show that the algorithm is well-posed and we prove its convergence by energy estimates and a Galerkin method. We then introduce an explicit scheme. We prove the convergence ...

In this note we consider residual-based a posteriori error estimation for finite element approximations of the transport equation. For the discretization we use piecewise affine continuous or discontinuous finite elements and symmetric stabilization of interior penalty type. The lowest order discontinuous Galerkin method using piecewise constant approximation is included as a special case. The ...

The minimization of functionals which are formed by an L2-term and a Total Variation (TV) term play an important role in mathematical imaging with many applications in engineering, medicine and art. The TV term is well known to preserve sharp edges in images. More precisely, we are interested in the minimization of a functional formed by a discrepancy term and a TV term. The first order derivat...

We present and analyze a high-order discontinuous Galerkin method for the space discretization of wave propagation model in thermo-poroelastic media. The proposed scheme supports general polytopal grids. Stability analysis $hp$-version error estimates suitable energy norms are derived semi-discrete problem. fully-discrete is then obtained based on employing an implicit Newmark-$\beta$ time inte...

Abstract We consider three different methods for the coupling of finite element method and boundary method, Bielak–MacCamy coupling, symmetric Johnson–Nédélec coupling. For each we provide discrete interior regularity estimates. As a consequence, are able to prove existence exponentially convergent $$\mathcal {H}$$ H </m...