Showing papers on "Meshfree methods published in 1989"
TL;DR: The nonconforming combination of Ritz-Galerkin and finite difference methods is presented for solving elliptic boundary value problems with singularities and shows that average errors of numerical solutions and their generalized derivatives can reach the convergence rate O(h2-δ), where h is the mesh spacing of uniform difference grids, and δ is an arbitrarily small, positive number.
Abstract: The nonconforming combination of Ritz-Galerkin and finite difference methods is presented for solving elliptic boundary value problems with singularities. The Ritz-Galerkin method is used in the subdomains including singularities, the finite difference method is used in the rest of the solution domain. Moreover, on the common boundary of two regions where two different methods are used, the continuity conditions are constrained only on the nodes of difference grids. Theoretical analysis and numerical experiments have shown that average errors of numerical solutions and their generalized derivatives can reach the convergence rate O(h2-δ), where h is the mesh spacing of uniform difference grids, and δ is an arbitrarily small, positive number. This convergence rate is better than O(h), obtained by the nonconforming combination of the Ritz-Galerkin and finite element methods.
11 citations
TL;DR: An algorithm is proposed for computing velocity fields in channels on the basis of the joint application of finite-elements and finite-difference methods by using an exponential approximation of the desired functions in the elements.
Abstract: An algorithm is proposed for computing velocity fields in channels on the basis of the joint application of finite-elements and finite-difference methods by using an exponential approximation of the desired functions in the elements.