We introduce a multitree-based adaptive wavelet Galerkin algorithm for space-time discretized linear parabolic partial differential equations, focusing on time-periodic problems. It is shown that the method converges with the best possible rate in linear complexity and can be applied for a wide range of wavelet bases. We discuss the implementational challenges arising from the Petrov-Galerkin n...

We present a space-time certified reduced basis method for long-time integration of parametrized noncoercive parabolic equations with quadratic nonlinearity. We first consider a finite element discretization based on discontinuous Galerkin time integration and introduce associated Petrov-Galerkin space-time trialand test-space norms which yields optimal and asymptotically mesh independent stabi...

In Meshless natura1 neighbour Petrov-Galerkin method, The natural neighbour interpolation is used as trial function and a weak form over the local polygonal sub-domains constructed by Delaunay triangular is used to obtain the discretized system of equilibrium equations, and it’s a new truly meshless method. This method simplified the formation of the equilibrium equations, facilitates the impos...

numerical solutions obtained by the meshless local petrov–galerkin (mlpg) method are presented for two-dimensional steady-state heat conduction problems. the mlpg method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. the penalty method is adopted to efficiently enforce the essential boundary co...

a truly meshless local petrov-galerkin (mlpg) method is developed for solving 3d elasto-static problems. using the general mlpg concept, this method is derived through the local weak forms of the equilibrium equations, by using test functions, namely, the heaviside function. the moving least squares (mls) are chosen to construct the shape functions, for the mlpg method. the penalty approximatio...

in this paper, three dimensional (3d) static and dynamic analysis of thick plates based on the meshless local petrov-galerkin (mlpg) is presented. using the kinematics of a three-dimensional continuum, the local weak form of the equilibrium equations is derived. a weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains by using a uni...