The meshless method based on the least-squares approach, the meshless weighted leastsquares (MWLS) method, is extended to solve conduction heat transfer problems. The MWLS formulation is first established for steady-state problems and then extended to unsteady-state problems with time-stepping schemes. Theoretical analysis and numerical examples indicate that larger time steps can be used in th...

FIGURE 2. Divergence of the arbitrary grid Legendre Galerkin method for improperly imposed initial conditions. Time-stable boundary conditions for nite-diierence schemes solving hyperbolic systems: methodology and application to high-order compact schemes, JCP 111, 220, (1994). 25 To initialize the problem, we must construct an approximation to the initial condition f(x), based on the grid poin...

We propose a goal-oriented mesh-adaptive algorithm for finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving saddle-point problem, this delivers stable continuous approximation to the solution each mesh instance and projection onto broken polynomial space, which is robust error estimator minimize discrete energy norm automatic refinement. In...

In this work, we propose a numerical method to obtain an unconditionally stable solution for the finite-difference time-domain (FDTD) method for the TE case. This new method does not utilize the customary explicit leapfrog time scheme of the conventional FDTD method. Instead we solve the time-domain Maxwell’s equations by expressing the transient behaviors in terms of weighted Laguerre polynomi...

a new approach for analyzing cracked problems in 2d orthotropic materials using the well-known element free galerkin method and orthotropic enrichment functions is proposed. the element free galerkin method is a meshfree method which enables discontinuous problems to be modeled efficiently. in this study, element free galerkin is extrinsically enriched by the recently developed crack-tip orthot...

The meshles.i method based on the least-squares approach, the rneshle.is weighted leastsquares (MWLS) method, is extended to soive conduction heat transfer problems. The MWLS formulation is first established for steady-state problems and then extended to unsteady-state problems with time-stepping schemes. Theoretiiai analy.us antl numerical examples indicate that larger time steps can be used i...

A general theory is given for discretized versions of the Galerkin method for solving Fredholm integral equations of the second kind. The discretized Galerkin method is obtained from using numerical integration to evaluate the integrals occurring in the Galerkin method. The theoretical framework that is given parallels that of the regular Galerkin method, including the error analysis of the sup...

The moving least-square technique is used to construct shape function in the Element Free Galerkin Method at present, but sometimes the algebra equations system obtained from the moving least-square approximation is ill-conditioned and the shape function needs large quantity of inverse operation. In this paper, the weighted orthogonal functions are used as basis ones, the application in the cal...

Residual-Based A Posteriori Error Estimates for $hp$-Discontinuous Galerkin Discretizations of the Biharmonic Problem

A numerical investigation is carried out in this work in order to evaluate the computational performance of a numerical model based on isogeometric analysis for applications on geometrically nonlinear elastodynamics. In the FEM (finite element method) practice, it is well known that the Newmark’s method is unconditionally stable for linear structural systems, but this characteristic is frequent...