A boundary element method has been developed for the analysis of 3D eddy current problems. This method is based on the boundary integral equation formulation with equivalent electric and magnetic currents and electric charge as unknowns. Linear shape functions, defined parametrically over a quadrilateral element, have been selected for the Galerkin’s method.

A new numerical scheme based on the H-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one spa...

We give a new analysis of Petrov-Galerkin finite element methods for solving linear singularly perturbed two-point boundary value problems without turning points. No use is made of finite difference methodology such as discrete maximum principles, nor of asymptotic expansions. On meshes which are either arbitrary or slightly restricted, we derive energy norm and L norm error bounds. These bound...

We establish pointwise andW−1 ∞ estimates for finite element methods for a class of second-order quasilinear elliptic problems defined on domains Ω in Rn. These estimates are localized in that they indicate that the pointwise dependence of the error on global norms of the solution is of higher order. Our pointwise estimates are similar to and rely on results and analysis techniques of Schatz fo...

In this article we derive error estimates for the Galerkin approximation of a general linear second order hyperbolic partial differential equation. The results can be applied to a variety of cases e.g. vibrating systems of linked elastic bodies. The results generalize the work of Baker [1] and also allow for viscous type damping. Splitting the proofs for the semidiscrete and fully discrete case...

We consider a mixed-boundary-value/interface problem for the elliptic operator P = − ∑ ij ∂i(aij∂ju) = f on a polygonal domain Ω ⊂ R2 with straight sides. We endowed the boundary of Ω partially with Dirichlet boundary conditions u = 0 on ∂DΩ, and partially with Neumann boundary conditions ∑ ij νiaij∂ju = 0 on ∂NΩ. The coefficients aij are piecewise smooth with jump discontinuities across the in...

A new variational (dis)continuous Galerkin finite element method is presented for linear free surface gravity water wave equations. In this method, the space-time finite element discretization is based on a discrete variational formulation analogous to a version of Luke’s variational principle. The finite element discretization results into a linear algebraic system of equations with a symmetri...

We present a space-time finite element formulation of the Navier-Stokes equations which is stabilized via the Galerkin/least-squares approach. The variational equation is based on the time discontinuous Galerkin method and is written in terms of the physical entropy variables over the moving and deforming space-time slabs. The formulation thus becomes analogous to the classical arbitrary Lagran...