A posteriori error estimates developed to drive hp-adaptivity for second-order reaction-diffusion equations are extended to fourth-order equations. A C1 hierarchical finite element basis is constructed from HermiteLobatto polynomials. A priori estimates of the error in several norms for both the interpolant and finite element solution are derived. In the latter case this requires a generalizati...

Neurules are a kind of hybrid rules that combine a symbolic (production rules) and a connectionist (adaline unit) representation. Each neurule is represented as an adaline unit. One way that the neurules can be produced is from training examples (empirical source knowledge). However, in certain application fields not all of the training examples are available a priori. A number of them become a...

In this paper, we present an approach integrating neurule-based and case-based reasoning. Neurules are a kind of hybrid rules that combine a symbolic (production rules) and a connectionist representation (adaline unit). Each neurule is represented as an adaline unit. One way that the neurules can be produced is from symbolic rules by merging the symbolic rules having the same conclusion. In thi...

The Adaline network [1] is a classic neural architecture whose learning rule is the famous least mean squares (LMS) algorithm (a.k.a. delta rule or Widrow-Hoff rule). It has been demonstrated that the LMS algorithm is optimal in H∞ sense since it tolerates small (in energy) disturbances, such as measurement noise, parameter drifting and modelling errors [2,3]. Such optimality of the LMS algorit...

Displacement finite element models of various beam theories have been developed using traditional finite element interpolations (i.e., Hermite cubic or equi-spaced Lagrange functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation φ and/or shear strain γxz, or in the integral form u...

In this thesis, we are mainly concerned with the numerical solution of the two dimensional Helmholtz equation by an adaptive Interior Penalty Discontinuous Galerkin (IPDG) method based on adaptively refined simplicial triangulations of the computational domain. The a posteriori error analysis involves a residual type error estimator consisting of element and edge residuals and a consistency err...

We consider the eeectiveness of adaptive nite-element methods for nding the nite element solutions of the parametrised semi-linear elliptic equation u+u+u 5 = 0; u > 0, where u 2 C 2 ((); for a domain IR 3 and u = 0 on the boundary of : This equation is important in analysis and it is known that there is a value 0 > 0 such that no solutions exist for < 0 and a singularity forms as ! 0. Furtherm...

We consider the eeectiveness adaptive nite-element methods for nding the nite element solutions of the parametrised semi-linear elliptic equation u+u+u 5 = 0; u > 0, where u 2 C 2 ((); for a domain IR 3 and u = 0 on the boundary of : This equation is important in analysis and it is known that there is a value 0 > 0 such that no solutions exist for < 0 and a singularity forms as ! 0. Furthermore...