Einige Eigenschaften der Lösung der Wellengleichung mit der Korrektion von Rayleigh
Elastic wave propagation in parallel: the Huygens' approach.
The use of parallel computers makes it feasible to simulate elastic waves throughout large heterogeneous structures, and new domain decomposition methods can be used to increase their efficiency and decrease the computing time spent in the simulation. In this paper we introduce a simple parallel algorithm for the propagation of elastic waves in complex heterogeneous media after a finite element discretization. This method performs more efficiently than classic domain decomposition techniques based...
Elementi Finiti Misti e Volumi Finiti per la soluzione del problema di flusso e trasporto di contaminanti radioattivi pesanti in mezzi porosi
Éléments finis et problèmes elliptiques dégénérés
Enabling numerical accuracy of Navier-Stokes-α through deconvolution and enhanced stability
We propose and analyze a finite element method for approximating solutions to the Navier-Stokes-alpha model (NS-α) that utilizes approximate deconvolution and a modified grad-div stabilization and greatly improves accuracy in simulations. Standard finite element schemes for NS-α suffer from two major sources of error if their solutions are considered approximations to true fluid flow: (1) the consistency error arising from filtering; and (2) the dramatic effect of the large pressure error on the...
Enabling numerical accuracy of Navier-Stokes-α through deconvolution and enhanced stability*
We propose and analyze a finite element method for approximating solutions to the Navier-Stokes-alpha model (NS-α) that utilizes approximate deconvolution and a modified grad-div stabilization and greatly improves accuracy in simulations. Standard finite element schemes for NS-α suffer from two major sources of error if their solutions are considered approximations to true fluid flow: (1) the consistency error arising from filtering; and (2) the dramatic effect of the large pressure error on the...
Energy error estimates for the projection-difference method with the Crank--Nicolson scheme for parabolic equations.
Energy estimates and numerical verification of the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system
We rigorously derive energy estimates for the second order vector wave equation with gauge condition for the electric field with non-constant electric permittivity function. This equation is used in the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system. Our numerical experiments illustrate efficiency of the modified hybrid scheme in two and three space dimensions when the method is applied for generation of backscattering data in the reconstruction...
Enhancement of Krylov subspace spectral methods by block Lanczos iteration.
Enthalpy model for heating, melting, and vaporization in laser ablation.
Entropy conditions and their numerical analogues for conservation laws
Entropy consistent, TVD methods with high accuracy for conservation laws.
Entropy production in second-order three-point schemes.
Équations d'évolution linéaires du second ordre et méthodes multipas
Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes
We consider the lowest-order Raviart–Thomas mixed finite element method for second-order elliptic problems on simplicial meshes in two and three space dimensions. This method produces saddle-point problems for scalar and flux unknowns. We show how to easily and locally eliminate the flux unknowns, which implies the equivalence between this method and a particular multi-point finite volume scheme, without any approximate numerical integration. The matrix of the final linear system is sparse, positive...
Error analysis of high-order splitting methods for nonlinear evolutionary Schrödinger equations and application to the MCTDHF equations in electron dynamics
In this work, the error behaviour of high-order exponential operator splitting methods for the time integration of nonlinear evolutionary Schrödinger equations is investigated. The theoretical analysis utilises the framework of abstract evolution equations on Banach spaces and the formal calculus of Lie derivatives. The general approach is substantiated on the basis of a convergence result for exponential operator splitting methods of (nonstiff) order p applied to the multi-configuration time-dependent...
Error control and adaptivity for a phase relaxation model
Error Control and Andaptivity for a Phase Relaxation Model
The phase relaxation model is a diffuse interface model with small parameter ε which consists of a parabolic PDE for temperature θ and an ODE with double obstacles for phase variable χ. To decouple the system a semi-explicit Euler method with variable step-size τ is used for time discretization, which requires the stability constraint τ ≤ ε. Conforming piecewise linear finite elements over highly graded simplicial meshes with parameter h are further employed for space discretization. A posteriori...
Error estimate for a fully discrete spectral scheme for Korteweg-de Vries-Kawahara equation
We are concerned with convergence of spectral method for the numerical solution of the initial-boundary value problem associated to the Korteweg-de Vries-Kawahara equation (Kawahara equation, in short), which is a transport equation perturbed by dispersive terms of the 3rd and 5th order. This equation appears in several fluid dynamics problems. It describes the evolution of small but finite amplitude long waves in various problems in fluid dynamics. These equations are discretized in space by the...
Error estimate for the characteristic method involving Oldroyd derivative in a tensorial transport problem.