High order explicit Runge-Kutta pairs for ephemerides of the solar system and the Moon.
High order finite difference schemes with application to wave propagation problems
High Order Methods for the Numerical Integration of Ordinary Differential Equations.
High Order P-Stable Formulae for the Numerical Integration of Periodic Initial Value Problems.
High order semi-lagrangian particle methods for transport equations: numerical analysis and implementation issues
This paper is devoted to the definition, analysis and implementation of semi-Lagrangian methods as they result from particle methods combined with remeshing. We give a complete consistency analysis of these methods, based on the regularity and momentum properties of the remeshing kernels, and a stability analysis of a large class of second and fourth order methods. This analysis is supplemented by numerical illustrations. We also describe a general approach to implement these methods in the context...
High order transmission conditions for thin conductive sheets in magneto-quasistatics
We propose transmission conditions of order 1, 2 and 3 approximating the shielding behaviour of thin conducting curved sheets for the magneto-quasistatic eddy current model in 2D. This model reduction applies to sheets whose thicknesses ε are at the order of the skin depth or essentially smaller. The sheet has itself not to be resolved, only its midline is represented by an interface. The computation is directly in one step with almost no additional cost. We prove the well-posedness w.r.t. to...
High order transmission conditions for thin conductive sheets in magneto-quasistatics
We propose transmission conditions of order 1, 2 and 3 approximating the shielding behaviour of thin conducting curved sheets for the magneto-quasistatic eddy current model in 2D. This model reduction applies to sheets whose thicknesses ε are at the order of the skin depth or essentially smaller. The sheet has itself not to be resolved, only its midline is represented by an interface. The computation is directly in one step with almost no additional cost. We prove the well-posedness w.r.t. to...
High resolution schemes for hyperbolic conservation laws
High-degree precision decomposition method for an evolution problem.
Higher Order Compatible Triangular Finite Elements.
Higher Order Convergence Results for the Rayleigh-Ritz Method Applied to Eigenvalue Problems: 2. Improved Error Bounds for Eigenfunctions.
Higher order Euler-like methods.
Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type
A nonlinear elliptic partial differential equation with homogeneous Dirichlet boundary conditions is examined. The problem describes for instance a stationary heat conduction in nonlinear inhomogeneous and anisotropic media. For finite elements of degree we prove the optimal rates of convergence in the -norm and in the -norm provided the true solution is sufficiently smooth. Considerations are restricted to domains with polyhedral boundaries. Numerical integration is not taken into account....
Higher order method for the numerical solution of the compressible Euler equations
Higher Order Methods for a Singularly Perturbed Problem.
Higher-dimensional central projection into 2-plane with visibility and applications
Higher-index differential-algebraic equations: analysis and numerical treatment
Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time
This paper deals with the numerical study of a nonlinear, strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. An Asymptotic-Preserving method is introduced in this paper, which is second-order accurate in both, temporal and spacial variables. The discretization in time is done using an L-stable Runge−Kutta scheme. The convergence of the method is shown to be independent of the anisotropy parameter , and this for fixed...
High-order compact implicit difference methods for parabolic equations in geodynamo simulation.
High-order finite difference schemes and Toeplitz based preconditioners for elliptic problems.