Finite element solution of boundary value problems with nonlocal jump conditions

Abstract

We consider stationary linear problems on non‐connected layers with distinct material properties. Well posedness and the maximum principle (MP) for the differential problems are proved. A version of the finite element method (FEM) is used for discretization of the continuous problems. Also, the MP and convergence for the discrete solutions are established. An efficient algorithm for solution of the FEM algebraic equations is proposed. Numerical experiments for linear and nonlinear problems are discussed.

Key words:

• finite element method
• nonlocal jump conditions
• well posedness
• maximum principle
• convergence

Notes

This research is supported by the Bulgarian National Fund of Science under Project VU‐MI‐106/2005