The multi-scale-finite-volume (MSFV) procedure for the approximate solution of elliptic problems with varying coefficients has been recently modified by introducing an iterative loop to achieve any desired level of accuracy (iterative MSFV, IMSFV). We further develop the iterative concept considering a Galerkin approach to define the coarse-scale problem, which is one of the key elements of the...

I n recent years, many numerical methods have been proposed for solving fuzzy linear integral equations. For example, in [10], the authors used the divided differences and finite differences methods for solving a parametric of the fuzzy Fredholm integral equations of the second kind. Also, in [9], a numerical method is proposed for the approximate solution of fuzzy linear Fredholm functional in...

An elliptic boundary value problem in the interior or exterior of a polygon is transformed into an equivalent rst kind boundary integral equation. Its Galerkin discretization with N degrees of freedom on the boundary with spline wavelets as basis functions is analyzed. A truncation strategy is presented which allows to reduce the number of nonzero elements in the stiiness matrix from O(N 2) to ...

A novel approach, radial basis function (RBF) mixed with domain decomposition method (DDM) based on Galerkin finite element method (FEM) has been introduced in our previous work. The proposed method divides the computational domain into a series of rectangular sub-domains, and each sub-domain is taken as a separate calculation area to get the solution expression and shape function by using the ...

This paper concerns with numerical approximations of solutions of fully nonlinear second order partial differential equations (PDEs). A new notion of weak solutions, called moment solutions, is introduced for fully nonlinear second order PDEs. Unlike viscosity solutions, moment solutions are defined by a constructive method, called the vanishing moment method, and hence, they can be readily com...

We propose a Wavelet-Galerkin scheme for the stationary NavierStokes equations based on the application of interpolating wavelets. To overcome the problems of nonlinearity, we apply the machinery of interpolating wavelets presented in [10] and [13] in order to obtain problem-adapted quadrature rules. Finally, we apply Newton’s method to approximate the solution in the given ansatz space, using ...

Thc devclopment of hp·version discontinuous Galerkin methods for hyperholic conservalion laws is presented in this work. A priori error estimates are dcrived for a model class of linear hyperbolic conservation laws. These estimates arc obtained using a ncw mesh-dependcnt norm that rel1ects thc dependcnce of the approximate solution on thc local element size and the local order of approximation....

In this paper we consider Galerkin-finite element methods that approximate the solutions of initial-boundary-value problems in one space dimension for parabolic and Schrödinger evolution equations with dynamical boundary conditions. Error estimates of optimal rates of convergence in L and H are proved for the accociated semidiscrete and fully discrete Crank-Nicolson-Galerkin approximations. The...

We consider a general elliptic Robin boundary value problem. Using orthogonal Coifman wavelets (Coiflets) as basis functions in the Galerkin method, we prove that the rate of convergence of an approximate solution to the exact one is O(2−nN ) in the H norm, where n is the level of approximation and N is the Coiflet degree. The Galerkin method needs to evaluate a lot of complicated integrals. We...

Compared with standard Galerkin finite element methods, mixed methods for second-order elliptic problems give readily available flux approximation, but in general at the expense of having to deal with a more complicated discrete system. This is especially true when conforming elements are involved. Hence it is advantageous to consider a direct method when finding fluxes is just a small part of ...