the rapid melting of a semi- infinite body due to the absorption of a cw laser beam radiation has been studied. the enthalpy technique for the solution of phase change problems has been used in an explicit finite difference form to calculate the transient temperature distribution in the semi-infinite body and the growth rate of the melt pool. the technique has been modified so that it is not ne...

1.3 We argue by contradiction. Thus we suppose that A is infinite and derive a contradiction. As a preliminary, observe that A is non-empty and hence has a ≤-least element, a first element. It also has a ≤∗-least element, a ≤-greatest element, a last element. For each element x let ↑x be the ≤-upper set generated by x, that is y ∈ ↑x ⇐⇒ x ≤ y for each y ∈ A. Consider the subset X ⊆ A given by x...

In this work, we analyse the Galerkin Infinite Element method for option pricing. The Infinite Element method is a very simple and efficient modification of the more common Finite Element method. It keeps the best features of Finite Elements, i.e. bandedness, easiness of programming, accuracy, and it is particularly useful when solving problems in unbounded domains. Three main aspects are consi...

Analysis of the stresses, displacements, and horizontal strains of the ground subsidence due to underground excavation in rocks can be accomplished by means of a hybridized higher order indirect boundary element/finite difference (BE/FD) formulation. A semi-infinite displacement discontinuity field is discretized (numerically) using the cubic displacement discontinuity elements (i.e. each highe...

Numerical methods (finite element methods) for the approximate solution of elliptic partial differential equations on unbounded domains are considered, and error bounds, with respect to the number of unknowns which have to be determined, are proven.

The scattering problem from time-harmonic waves by a Neumann type crack in R is considered. A PML technique is used for solving the problem with a bounded domain instead of the infinite domain. A coupled finite-infinite element method is employed in the computation. Because of the singularity of the solution, the infinite element method is used near the crack tip. An error analysis is presented...