Radial minimizer of a -Ginzburg-Landau type functional with normal impurity inclusion.
Radial minimizer of a variant of the -Ginzburg-Landau functional.
Regularity analysis for systems of reaction-diffusion equations
This paper is devoted to the study of the regularity of solutions to some systems of reaction–diffusion equations. In particular, we show the global boundedness and regularity of the solutions in one and two dimensions. In addition, we discuss the Hausdorff dimension of the set of singularities in higher dimensions. Our approach is inspired by De Giorgi’s method for elliptic regularity with rough coefficients. The proof uses the specific structure of the system to be considered and is not a mere...
Relaxation approximations and bounded variation estimates for some partial differential equations.
Resolvent estimates for scalar fields with electromagnetic perturbation.
Robust exponential attractors for singularly perturbed phase-field type equations.
Robust local problem error estimation for a singularly perturbed problem on anisotropic finite element meshes
Singularly perturbed problems often yield solutions with strong directional features, e.g. with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation. To this end we present a new robust error estimator for a singularly perturbed reaction–diffusion problem. In contrast to conventional estimators, our proposal is suitable for anisotropic finite element...
Robust local problem error estimation for a singularly perturbed problem on anisotropic finite element meshes
Singularly perturbed problems often yield solutions with strong directional features, e.g. with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation. To this end we present a new robust error estimator for a singularly perturbed reaction-diffusion problem. In contrast to conventional estimators, our proposal is suitable for anisotropic finite element...