We present a systematic method for developing low order nonlinear models from physically based, large scale finite element models of rapid thermal processing (RTP) systems. These low order models are extracted from transient results of a detailed finite element model using the proper orthogonal decomposition (POD) method. Eigenfunctions obtained from the POD method are then used as basis functi...

Starting from the generalized Lax-Milgram theorem and from the fact that the approximation error is minimized when the continuity and inf– sup constants are unity, we develop a theory that provably delivers well-posed approximation methods with unity continuity and inf–sup constants for numerical solution of linear partial differential equations. We demonstrate our single-framework theory on sc...

(2000) Meshless local Petrov–Galerkin (MLPG) method in combination with finite element and boundary element approaches. Abstract The Meshless Local Petrov-Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using Moving Least Squares (MLS) interpolants. It is, however, computationally expensive for some problems. A coupled MLPG/Finite Element ...

This paper presents the application of the hybrid finite element-element free Galerkin (FE-EFG) method for the forward and inverse problems of electrical impedance tomography (EIT). The proposed method is based on the complete electrode model. Finite element (FE) and element-free Galerkin (EFG) methods are accurate numerical techniques. However, the FE technique has meshing task problems and th...

We construct stochastic Galerkin approximations to the solution of a first-order system of PDEs with random coefficients. Under the standard finite-dimensional noise assumption, we transform the variational saddle point problem to a parametric deterministic one. Approximations are constructed by combining mixed finite elements on the computational domain with M -variate tensor product polynomia...

In this paper a theoretical framework for the Galerkin finite element approximation to the steady state fractional advection dispersion equation is presented. Appropriate fractional derivative spaces are defined and shown to be equivalent to the usual fractional dimension Sobolev spaces H. Existence and uniqueness results are proven, and error estimates for the Galerkin approximation derived. N...