FEM in MATLAB

Therefore for each node p we have an algebraic equation 

For a source term with no field-dependence, (6.228) is a sparse linear system. If not, it must be solved with Newton s method however, the Jacobian matrix is also sparse. 

we have considered only diffusive transport however, it is not difficult to extend the method to include convective transport as well. The choice of linear shape functions used above results in a system of algebraic equations with similar accuracy to central finite difference approximations and shares the tendency of CDS to exhibit unphysical oscillations when convection is strong. The oscillations are reduced by mesh refinement (to reduce the local Pec let number) or by adding additional numerical diffusion, especially in the streamline direction. Upwind versions of FEM are obtained by biasing the shape functions to weight more heavily the upstream direction. Such subjects are beyond the scope of this chapter, and the reader is referred to a dedicated text on FEM such as Akin (1994). The relationship between FEM with linear shape functions and CDS finite differences is examined in the supplemental material in the accompanying website for the case of the 1-D convection/diffusion equation. 

we have only a single field, but the solver can treat multiple fields and field-dependent source terms (if we set the nlin flag to on or use pdenonlin). Type doc adaptmesh for further details. There are also lower-level commands available that perform isolated tasks such as assembling the various matrices, and interpolating fields from node values however, the use of such routines is beyond the scope of this text. Finally, routines 

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