Error estimation of pseudospectral method for solving the barotropic vorticity equation.
Error of the two-step BDF for the incompressible Navier-Stokes problem
The incompressible Navier-Stokes problem is discretized in time by the two-step backward differentiation formula. Error estimates are proved under feasible assumptions on the regularity of the exact solution avoiding hardly fulfillable compatibility conditions. Whereas the time-weighted velocity error is of optimal second order, the time-weighted error in the pressure is of first order. Suboptimal estimates are shown for a linearisation. The results cover both the two- and three-dimensional case....
Error of the two-step BDF for the incompressible Navier-Stokes problem
The incompressible Navier-Stokes problem is discretized in time by the two-step backward differentiation formula. Error estimates are proved under feasible assumptions on the regularity of the exact solution avoiding hardly fulfillable compatibility conditions. Whereas the time-weighted velocity error is of optimal second order, the time-weighted error in the pressure is of first order. Suboptimal estimates are shown for a linearisation. The results cover both the two- and three-dimensional...
Estimation of a temporally and spatially varying diffusion coefficinet in a parabolic system by an augmented Lagrangian technique.
Estimation of the conductivity in the one-phase Stefan problem : numerical results
Étude numérique des oscillations des systèmes semi-linéaires
Étude numérique des pôles de résonance associés à la diffraction d'ondes acoustiques et élastiques par un obstacle en dimension 2
Euler characteristic Galerkin scheme with recovery
Explicit difference schemes for nonlinear differential functional parabolic equations with time dependent coefficients-convergence analysis
We study the initial-value problem for parabolic equations with time dependent coefficients and with nonlinear and nonlocal right-hand sides. Nonlocal terms appear in the unknown function and its gradient. We analyze convergence of explicit finite difference schemes by means of discrete fundamental solutions.
Explicit Finite Element Schemes for First Order Symmetric Hyperbolic Systems.
Explicit Runge-Kutta Formulas with Increased Stability Boundaries.
Exponentially convergent parallel discretization methods for the first order evolution equations.
Extrapolation Applied to Certain Discretization Methods Solving the Initial Value Problem for Hyperbolic Differential Equations.
Extrapolation to the Limit for Numerical Solutions of Hyperbolic Equations.
Facilitating the Adoption of Unstructured High-Order Methods Amongst a Wider Community of Fluid Dynamicists
Theoretical studies and numerical experiments suggest that unstructured high-order methods can provide solutions to otherwise intractable fluid flow problems within complex geometries. However, it remains the case that existing high-order schemes are generally less robust and more complex to implement than their low-order counterparts. These issues, in conjunction with difficulties generating high-order meshes, have limited the adoption of high-order...
Finite Difference Approximation of Strong Solutions of a Parabolic Interface Problem on Disconnected Domains
Finite difference approximations for a class of nonlocal parabolic equations.
Finite difference approximations for nonlinear first order partial differential equations.
Finite difference approximations for partial differential equations with rapidly oscillating coefficients
Finite difference discretization of the Kuramoto-Sivashinsky equation.