Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation

Efficient discretization of Laplace boundary integral equations on polygonal domains

We describe a numerical procedure for the construction of quadrature formulae suitable for the efficient discretization of boundary integral equations over very general curve segments. While the procedure has applications to the solution of boundary value problems on a wide class of complicated domains, we concentrate in this paper on a particularly simple case: the rapid solution of boundary v...

Analysis of the Finite Element Method for Transmission/mixed Boundary Value Problems on General Polygonal Domains

We study theoretical and practical issues arising in the implementation of the Finite Element Method for a strongly elliptic second order equation with jump discontinuities in its coefficients on a polygonal domain Ω that may have cracks or vertices that touch the boundary. We consider in particular the equation − div(A∇u) = f ∈ H(Ω) with mixed boundary conditions, where the matrix A has variab...

Integral Equation Formulations for Geodetic Mixed Boundary Value Problems

We consider mixed boundary value problems in Physical Geodesy and study possibilities in order to transform them into a system of integral equations over the boundary of the domain. The system of integral equations can be solved numerically, by, e.g. boundary element methods, provided that (a) the mixed boundary value problem is uniquely solvable, (b) the system of integral equations is equival...

Boundary value problems for mixed type equations and applications

Boundary Value Problems for Nonlinear Fractional Differential Equations and Inclusions with Nonlocal and Integral Boundary Conditions

In this paper, we study a class of boundary value problems of nonlinear fractional differential equations and inclusions with nonlocal and integral boundary conditions. Some new existence and uniqueness results are obtained by using a variety of fixed point theorems. Examples are given to illustrate the results.