A new class of fitted mesh finite element method for convection-diffusion-reaction problems

Authors:
Kailash C. Patidar
Affiliations:
Department of Mathematics and Applied Mathematics, University of the Western Cape, Bellville, South Africa
Venue:
Neural, Parallel & Scientific Computations
Year:
2010

Citing 6
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Abstract

We design a novel finite element method for a class of singularly perturbed two-point boundary value problems. Using the intrinsic singular feature of the solution and some a priori error estimates, we design the method, based upon a finite element discretization on a suitably refined mesh. This new method is referred as Mesh Refinement Finite Element Method and is proved to be ε-uniformly convergent in appropriate norms. Optimal values of the mesh generating parameter (referred to as v) is obtained via a priori error analysis. These optimal values are then considered as main indicators in identifying a fixed value of v that can provide reliable mesh on which the finite element method provides parameter robust numerical results.