Crack jump conditions for elliptic problems

Immersed Finite Element Methods for Elliptic Interface Problems with Non-homogeneous Jump Conditions

Abstract. This paper is to develop immersed finite element (IFE) functions for solving second order elliptic boundary value problems with discontinuous coefficients and non-homogeneous jump conditions. These IFE functions can be formed on meshes independent of interface. Numerical examples demonstrate that these IFE functions have the usual approximation capability expected from polynomials emp...

Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Nonhomogeneous Jump Conditions

In this work, a class of new finite-element methods, called immersed-interface finite-element methods, is developed to solve elliptic interface problems with nonhomogeneous jump conditions. Simple non–body-fitted meshes are used. A single function that satisfies the same nonhomogeneous jump conditions is constructed using a level-set representation of the interface. With such a function, the di...

Domain Decomposition with Subdomain CCG for Material Jump Elliptic Problems

Landesman-Laser Conditions and Quasilinear Elliptic Problems

In this paper we consider two elliptic problems. The first one is a Dirichlet problem while the second is Neumann. We extend all the known results concerning Landesman-Laser conditions by using the Mountain-Pass theorem with the Cerami (PS) condition.

Elliptic Boundary Problems with Relaxed Conditions

We use the Fredholm property of the operator associated with an elliptic boundary problem on a compact manifold with boundary to prove solvability results for a “relaxed” problem where the equation or the boundary conditions are “relaxed” (not required to hold) on a non-empty open set. We also formulate a generalization of the Fredholm property to the case when the problem is considered on a no...