A mathematical analysis of thermal explosions.
A mathematical and computational framework for reliable real-time solution of parametrized partial differential equations
We present in this article two components: these components can in fact serve various goals independently, though we consider them here as an ensemble. The first component is a technique for the rapid and reliable evaluation prediction of linear functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential features are (i) (provably) rapidly convergent global reduced–basis approximations — Galerkin projection onto a space spanned...
A Mathematical and Computational Framework for Reliable Real-Time Solution of Parametrized Partial Differential Equations
We present in this article two components: these components can in fact serve various goals independently, though we consider them here as an ensemble. The first component is a technique for the rapid and reliable evaluation prediction of linear functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential features are (i) (provably) rapidly convergent global reduced–basis approximations — Galerkin projection onto a space WN spanned...
A maximum principle for biharmonic functions in Lipschitz and C1 domains.
A maximum principle for mean-curvature type elliptic inequalities
A maximum principle for systems with variational structure and an application to standing waves
We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differential equations on a periodic domain. The main tool is a replacement lemma which has as a corollary a maximum principle for minimizers.
A method for solving a boundary value problem for a partial differential equation of elliptic type.
A minimax formula for the principal eigenvalues of Dirichlet problems and its applications.
A minimax inequality for a class of functionals and applications to the existence of solutions for two-point boundary-value problems.
A minimax principle, index of the critical point, and existence of sign-changing solutions to elliptic boundary value problems.
A minimization problem arising from prescribing scalar curvature functions.
A minimization problem associated with elliptic systems of Fitz–Hugh–Nagumo type
A mixed boundary value problem for Laplace's equation involving a nearly circular disk.
A mixed boundary value problem for the Laplace equation in an angle (2nd part)
A mixed boundary value problem for the Laplace equation in an angle (1st part)
A mixed finite element method close to the equilibrium model (Preliminary communication)
A mixed finite element method close to the equilibrium model applied to plane elastostatics
A mixed finite element method for a weighted elliptic problem
A mixed method for 4th order problems using linear finite elements
A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media
This paper proposes and analyzes a BEM-FEM scheme to approximate a time-harmonic diffusion problem in the plane with non-constant coefficients in a bounded area. The model is set as a Helmholtz transmission problem with adsorption and with non-constant coefficients in a bounded domain. We reformulate the problem as a four-field system. For the temperature and the heat flux we use piecewise constant functions and lowest order Raviart-Thomas elements associated to a triangulation approximating the...