Error analysis of the nonlinear multigrid method of the second kind
The Rothe-Galerkin method is used for discretization. The rate of convergence in for the approximate solution of a quasilinear parabolic equation with a Volterra operator on the right-hand side is established.
Non-linear singular integral equations are investigated in connection with some basic applications in two-dimensional fluid mechanics. A general existence and uniqueness analysis is proposed for non-linear singular integral equations defined on a Banach space. Therefore, the non-linear equations are defined over a finite set of contours and the existence of solutions is investigated for two different kinds of equations, the first and the second kind. Moreover, the existence of solutions is further...
Galerkin discretizations of integral equations in require the evaluation of integrals where S(1),S(2) are d-simplices and g has a singularity at x = y. We assume that g is Gevrey smooth for xy and satisfies bounds for the derivatives which allow algebraic singularities at x = y. This holds for kernel functions commonly occurring in integral equations. We construct a family of quadrature rules using N function evaluations of g which achieves exponential convergence |I – | ≤C exp(–rNγ) with...
Galerkin discretizations of integral equations in require the evaluation of integrals where S(1),S(2) are d-simplices and g has a singularity at x = y. We assume that g is Gevrey smooth for xy and satisfies bounds for the derivatives which allow algebraic singularities at x = y. This holds for kernel functions commonly occurring in integral equations. We construct a family of quadrature rules using N function evaluations of g which achieves exponential convergence |I – | ≤C exp(–rNγ) with...