Convergence of numerical algorithms for semilinear hyperbolic system
Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem
We study convergence of formal power series along families of formal or analytic vector fields. One of our results says that if a formal power series converges along a family of vector fields, then it also converges along their commutators. Using this theorem and a result of T. Morimoto, we prove analyticity of formal solutions for a class of nonlinear singular PDEs. In the proofs we use results from control theory.
Convergence of Rothe's method in Hölder spaces
The convergence of Rothe’s method in Hölder spaces is discussed. The obtained results are based on uniform boundedness of Rothe’s approximate solutions in Hölder spaces recently achieved by the first author. The convergence and its rate are derived inside a parabolic cylinder assuming an additional compatibility conditions.
Convergence of solutions of generalized Korteweg-de Vries-Burgers equations to those of first order equations
Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems
We consider the symmetric FEM-BEM coupling for the numerical solution of a (nonlinear) interface problem for the 2D Laplacian. We introduce some new a posteriori error estimators based on the (h − h/2)-error estimation strategy. In particular, these include the approximation error for the boundary data, which allows to work with discrete boundary integral operators only. Using the concept of estimator reduction, we prove that the proposed adaptive...
Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems
We consider the symmetric FEM-BEM coupling for the numerical solution of a (nonlinear) interface problem for the 2D Laplacian. We introduce some new a posteriori error estimators based on the (h − h/2)-error estimation strategy. In particular, these include the approximation error for the boundary data, which allows to work with discrete boundary integral operators only. Using the concept of estimator reduction, we prove that the proposed adaptive...
Convergence of the boundary control for the wave equation in domains with holes of critical size.
Convergence of the coincidence set in the homogenization of the obstacle problem
Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems
Numerical solution of fractional order diffusion problems with homogeneous Dirichlet boundary conditions is investigated on a square domain. An appropriate extension is applied to have a well-posed problem on and the solution on the square is regarded as a localization. For the numerical approximation a finite difference method is applied combined with the matrix transformation method. Here the discrete fractional Laplacian is approximated with a matrix power instead of computing the complicated...
Convergence of the Multigrid Full Approximation Scheme for a Class of Elliptic Mildly Nonlinear Boundary Value Problems.
Convergence of the Multilevel Full Approximation Scheme including the V-Cycle.
Convergence of the Nonconforming Wilson Element for Arbitrary Quadrilateral Meshes.
Convergence of the 'relativistic' heat equation to the heat equation as c → ∞.
We prove that the entropy solutions of the so-called relativistic heat equation converge to solutions of the heat equation as the speed of light c tends to ∞ for any initial condition u0 ≥ 0 in L1(RN) ∩ L∞(RN).
Convergence of the rotating fluids system in a domain with rough boundaries
We consider a rotating fluid in a domain with rough horizontal boundaries. The Rossby number, kinematic viscosity and roughness are supposed of characteristic size . We prove a convergence theorem on solutions of Navier-Stokes Coriolis equations, as goes to zero, in the well prepared case. We show in particular that the limit system is a two-dimensional Euler equation with a nonlinear damping term due to boundary layers. We thus generalize the results obtained on flat boundaries with the classical...
Convergence of the Schrödinger-Poisson system to the Euler equations under the influence of a large magnetic field
In this paper, we prove the convergence of the current defined from the Schrödinger-Poisson system with the presence of a strong magnetic field toward a dissipative solution of the Euler equations.
Convergence of the Schrödinger-Poisson system to the Euler equations under the influence of a large magnetic field
In this paper, we prove the convergence of the current defined from the Schrödinger-Poisson system with the presence of a strong magnetic field toward a dissipative solution of the Euler equations.
Convergence of -cycle and -cycle multigrid methods for the biharmonic problem using the Morley element.
Convergence properties of the finite difference method for solving variational inequalities
Convergence Properties of the Runge-Kutta-Chebyshev Method.
Convergence rate estimate for a domain decomposition method.