Runge-Kutta methods for parabolic equations with nonsmooth initial data
Schéma des différences finies pour un système d'équations paraboliques non linéaires avec dérivées mixtes
Schema explicite des différences finies pour un système d'équations non linéaires du type parabolique avec des conditions aux limites non linéaires
Semidiscretization for a nonlocal parabolic problem.
Semigroup formulation of Rothe's method: application to parabolic problems
A semilinear parabolic equation in a Banach space is considered. The purpose of this paper is to show the dependence of an error estimate for Rothe's method on the regularity of initial data. The proofs are done using a semigroup theory and Taylor spectral representation.
Sharp stability estimates for hyperbolic conservation laws.
Skipping transition conditions in a posteriori error estimates for finite element discretizations of parabolic equations
In this paper we derive a posteriori error estimates for the heat equation. The time discretization strategy is based on a θ-method and the mesh used for each time-slab is independent of the mesh used for the previous time-slab. The novelty of this paper is an upper bound for the error caused by the coarsening of the mesh used for computing the solution in the previous time-slab. The technique applied for deriving this upper bound is independent of the problem and can be generalized to other time...
Smoothing effect and discretization in time to semilinear parabolic equations with nonsmooth data
The purpose of this paper is to derive the error estimates for discretization in time of a semilinear parabolic equation in a Banach space. The estimates are given in the norm of the space for when the initial condition is not regular.
Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations.
Solution of time-dependent advection-diffusion problems with the sparse-grid combination technique and a Rosenbrock solver.
Some abstract error estimates of a finite volume scheme for a nonstationary heat equation on general nonconforming multidimensional spatial meshes
A general class of nonconforming meshes has been recently studied for stationary anisotropic heterogeneous diffusion problems, see Eymard et al. (IMA J. Numer. Anal. 30 (2010), 1009–1043). Thanks to the basic ideas developed in the stated reference for stationary problems, we derive a new discretization scheme in order to approximate the nonstationary heat problem. The unknowns of this scheme are the values at the centre of the control volumes, at some internal interfaces, and at the mesh points...
Some fast finite-difference solvers for two-dimensional evolutionary equations on special domains
The author proves the existence of the asymptotic error expansion to the Peaceman-Rachford finite-difference scheme for the first boundary value problem of the two-dimensional evolationary equation on the so-called uniform and nearly uniform domains. This expansion leads, by Richardson extrapolation, to a simple process for accelerating the convergence of the method. A numerical example is given.
Some new error estimates for finite element methods for second order hyperbolic equations using the Newmark method
We consider a family of conforming finite element schemes with piecewise polynomial space of degree in space for solving the wave equation, as a model for second order hyperbolic equations. The discretization in time is performed using the Newmark method. A new a priori estimate is proved. Thanks to this new a priori estimate, it is proved that the convergence order of the error is in the discrete norms of and , where and are the mesh size of the spatial and temporal discretization, respectively....
Some partial differential Volterra equation problems arising in viscoelasticity
Some remarks on the Galerkin approximation of parabolic equations
Space-time discontinuos Galerkin method for solving nonstationary convection-diffusion-reaction problems
The paper presents the theory of the discontinuous Galerkin finite element method for the space-time discretization of a linear nonstationary convection-diffusion-reaction initial-boundary value problem. The discontinuous Galerkin method is applied separately in space and time using, in general, different nonconforming space grids on different time levels and different polynomial degrees and in space and time discretization, respectively. In the space discretization the nonsymmetric interior...
Stabile Mehrschichtverfahren für parabolische Evolutionsgleichungen.
Stability and Accuracy for Implicit Semidiscretizations of Hyperbolic Problems.
Study of convergence of the projection-difference method for hyperbolic equations.
Sur une famille bi-parométriques de schémas des différences finies pour l'équation parabolique sans dérivées mixtes