Finite Dimensional Approximation of Nonlinear Problems. Part II : Limit Points.
Finite Dimensional Approximation of Nonlinear Problems. Part III : Simple Bifurcation Points.
Finite element approximation of a model reaction - diffusion problem with a non-Lipschitz nonlinearity.
Finite element approximation of nonlinear elliptic problems with discontinuous coefficients
Finite element approximation of nonlinear elliptic problems with discontinuous coefficients
Finite Element Error Estimates for Non-Linear Elliptic Equations of Monotone Type.
Finite Element Solution of Nonlinear Elliptic Problems.
Finite element solutions for radiation cooling problems with nonlinear boundary conditions
Finite volume schemes for fully non-linear elliptic equations in divergence form
We construct finite volume schemes, on unstructured and irregular grids and in any space dimension, for non-linear elliptic equations of the -laplacian kind: (with ). We prove the existence and uniqueness of the approximate solutions, as well as their strong convergence towards the solution of the PDE. The outcome of some numerical tests are also provided.
Finite volume schemes for fully non-linear elliptic equations in divergence form
We construct finite volume schemes, on unstructured and irregular grids and in any space dimension, for non-linear elliptic equations of the p-Laplacian kind: -div(|∇u|p-2∇u) = ƒ (with 1 < p < ∞). We prove the existence and uniqueness of the approximate solutions, as well as their strong convergence towards the solution of the PDE. The outcome of some numerical tests are also provided.
Finite volume schemes for the p-laplacian on cartesian meshes
This paper is concerned with the finite volume approximation of the p-laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh’s interfaces is needed in order to discretize the p-laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally...
Finite volume schemes for the p-Laplacian on Cartesian meshes
This paper is concerned with the finite volume approximation of the p-Laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh's interfaces is needed in order to discretize the p-Laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally...
Fourth-order nonlinear elliptic equations with critical growth
In this paper we consider a nonlinear elliptic equation with critical growth for the operator in a bounded domain . We state some existence results when . Moreover, we consider , expecially when is a ball in .
Free boundary problems and transonic shocks for the Euler equations in unbounded domains
We establish the existence and stability of multidimensional transonic shocks (hyperbolic-elliptic shocks), which are not nearly orthogonal to the flow direction, for the Euler equations for steady compressible potential fluids in unbounded domains in . The Euler equations can be written as a second order nonlinear equation of mixed hyperbolic-elliptic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the...
Free Boundary Problems with Nonlinear Source Terms.
Further qualitative properties for elliptic equations in unbounded domains