A new non-conforming finite element discretization methodology for second order elliptic partial differential equations involving higher order local absorbing boundary conditions in 2D and 3D is proposed. The novelty of the approach lies in the application of C-continuous finite element spaces, which is the standard discretization of second order operators, to the discretization of boundary dif...

This paper poses two magnetostatic problems in cylindrical coordinates with different permeabilities for each region. In the first problem the boundary condition of the second kind is used while in the second one, the boundary condition of the third kind is utilized. These problems are solved using the finite element and finite difference methods. In second problem, the results of the finite di...

The complex variable boundary element method, CVBEM, employs the Cauchy integral with any complex variable (e.g., complex potential, complex flux, or complex velocity) to solve boundary value problems. The CVBEM formulation is consistent with the primal and dual solutions of the boundary integral equation, as well as the analytic element method. The resulting problem is overdetermined because t...

The indirect boundary element method for the Helmholtz equation in three dimensions is of great interest and practical value for many problems in acoustics as it is capable of treating infinitely thin plates and allows coupling of interior and exterior scattering problems. In the present paper we provide a new approach for treatment of boundary integrals, including hypersingular, singular, and ...

We present an immersed finite element technique for boundary-value and interface problems from nonlinear solid mechanics. Its key features are the implicit representation of domain boundaries and interfaces, the use of Nitsche’s method for the incorporation of boundary conditions, accurate numerical integration based on marching tetrahedrons and cut-element stabilisation by means of extrapolati...

This paper presents a ‘‘simple’’ boundary element method for transient heat conduction in functionally graded materials, which leads to a boundary-only formulation without any domain discretization. For a broad range of functional material variation (quadratic, exponential and trigonometric) of thermal conductivity and specific heat, the non-homogeneous problem can be transformed into the stand...