Reaction diffusion equations and quadratic convergence.
Reflectionless boundary propagation formulas for partial wave solutions to the wave equation.
Reproducing kernel methods for solving linear initial-boundary-value problems.
Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices
This article discusses the numerical approximation of time dependent Ginzburg-Landau equations. Optimal error estimates which are robust with respect to a large Ginzburg-Landau parameter are established for a semi-discrete in time and a fully discrete approximation scheme. The proofs rely on an asymptotic expansion of the exact solution and a stability result for degree-one Ginzburg-Landau vortices. The error bounds prove that degree-one vortices can be approximated robustly while unstable higher...
Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices
This article discusses the numerical approximation of time dependent Ginzburg-Landau equations. Optimal error estimates which are robust with respect to a large Ginzburg-Landau parameter are established for a semi-discrete in time and a fully discrete approximation scheme. The proofs rely on an asymptotic expansion of the exact solution and a stability result for degree-one Ginzburg-Landau vortices. The error bounds prove that degree-one vortices can be approximated robustly while unstable higher...
Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation.
Rothe time-discretization method for a nonlocal problem arising in thermoelasticity.
Runge Property and Multiplicity of Solutions for Elliptic Equations in IRN with a Monotone Nonlinearity.