Our aim in this article is to prove the existence of solutions for a Cahn–Hilliard–Navier–Stokes ... more Our aim in this article is to prove the existence of solutions for a Cahn–Hilliard–Navier–Stokes system based on the Oono model and with singular potentials (and, in particular, the thermodynamically relevant logarithmic potentials). The Oono model was proposed in order to account for long-ranged (nonlocal) interactions, but also to simplify numerical simulations.
In this article, we formulate a model describing the evolution of thickness of a grounded shallow... more In this article, we formulate a model describing the evolution of thickness of a grounded shallow ice sheet. The thickness of the ice sheet is constrained to be nonnegative. This renders the problem under consideration an obstacle problem. A rigorous analysis shows that the model is thus governed by a set of variational inequalities that involve nonlinearities in the time derivative and in the elliptic term, and that it admits solutions, whose existence is established by means of a semi-discrete scheme and the penalty method.
This article is concerned with the nonlinear singular perturbation problem due to small diffusivi... more This article is concerned with the nonlinear singular perturbation problem due to small diffusivity in nonlinear evolution equations of Chaffee-Infante type. The boundary layer appearing at the boundary of the domain is fully described by a corrector which is “explicitly” constructed. This corrector allows us to obtain convergence in Sobolev spaces up to the boundary. AMS Subject Classification. 35B40, 35C20, 35Q30, 46N20, 76D10
2 Abstract. We study the consistency and convergence of the cell-centered Finite Vol- ume (FV) ex... more 2 Abstract. We study the consistency and convergence of the cell-centered Finite Vol- ume (FV) external approximation of H 1 0 (Ω), where a 2D polygonal domain Ω is dis- cretized by a mesh of convex quadrilaterals. The discrete FV derivatives are dened by using the so-called Taylor Series Expansion Scheme (TSES). By introducing the Finite Difference (FD) space associated with the FV space, and comparing the FV and FD spaces, we prove the convergence of the FV external approximation by using the consistency and convergence of the FD method. As an application, we construct the discrete FV approximation of some typical elliptic equations, and show the convergence of the discrete FV approximations to the exact solutions.
Our aim in this article is to prove the existence of solutions for a Cahn–Hilliard–Navier–Stokes ... more Our aim in this article is to prove the existence of solutions for a Cahn–Hilliard–Navier–Stokes system based on the Oono model and with singular potentials (and, in particular, the thermodynamically relevant logarithmic potentials). The Oono model was proposed in order to account for long-ranged (nonlocal) interactions, but also to simplify numerical simulations.
In this article, we formulate a model describing the evolution of thickness of a grounded shallow... more In this article, we formulate a model describing the evolution of thickness of a grounded shallow ice sheet. The thickness of the ice sheet is constrained to be nonnegative. This renders the problem under consideration an obstacle problem. A rigorous analysis shows that the model is thus governed by a set of variational inequalities that involve nonlinearities in the time derivative and in the elliptic term, and that it admits solutions, whose existence is established by means of a semi-discrete scheme and the penalty method.
This article is concerned with the nonlinear singular perturbation problem due to small diffusivi... more This article is concerned with the nonlinear singular perturbation problem due to small diffusivity in nonlinear evolution equations of Chaffee-Infante type. The boundary layer appearing at the boundary of the domain is fully described by a corrector which is “explicitly” constructed. This corrector allows us to obtain convergence in Sobolev spaces up to the boundary. AMS Subject Classification. 35B40, 35C20, 35Q30, 46N20, 76D10
2 Abstract. We study the consistency and convergence of the cell-centered Finite Vol- ume (FV) ex... more 2 Abstract. We study the consistency and convergence of the cell-centered Finite Vol- ume (FV) external approximation of H 1 0 (Ω), where a 2D polygonal domain Ω is dis- cretized by a mesh of convex quadrilaterals. The discrete FV derivatives are dened by using the so-called Taylor Series Expansion Scheme (TSES). By introducing the Finite Difference (FD) space associated with the FV space, and comparing the FV and FD spaces, we prove the convergence of the FV external approximation by using the consistency and convergence of the FD method. As an application, we construct the discrete FV approximation of some typical elliptic equations, and show the convergence of the discrete FV approximations to the exact solutions.
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Papers by Roger Temam