The solution to the elastodynamic equation in exterior of a polyhedral domain or screen exhibits singular behavior from corners and edges. detailed expansion singularities implies quasi-optimal estimates for piecewise polynomial approximations Dirichlet trace traction. results are applied hp graded versions time boundary element method weakly hypersingular integral equations. Numerical examples...

out, R will represent an associative ring with center Z(R). As usual the commutator xy−yx will be denoted by [x,y]. We will use basic commutator identities [xy,z] = [x,z]y+x[y,z] and [x,yz]= [x,y]z+y[x,z]. Recall that a ring R is prime if aRb = (0) implies that a = 0 or b = 0, and is semiprime if aRa = (0) implies a = 0. An additive mapping x x∗ on a ring R is called involution in case (xy)∗ = ...

Abstract Let ℛ be a semiprime ring with unity e and ϕ , φ automorphisms of ℛ. In this paper it is shown that if satisfies 2

In this work we are concerned with the numerical solution of a nonlinear weakly singular Volterra integral equation with a nonsmooth solution. We investigate the application of product integration methods and a detailed analysis of the Trapezoidal method is given. In order to improve the numerical results we consider extrapolation procedures and collocation methods based on graded meshes. Sever...

Abstract. A numerical method for a two-dimensional curl-curl and grad-div problem is studied in this paper. It is based on a discretization using weakly continuous P1 vector fields and includes two consistency terms involving the jumps of the vector fields across element boundaries. Optimal convergence rates (up to an arbitrary positive ) in both the energy norm and the L2 norm are established ...