A class of finite-element methods for singularly perturbed second-order differential equations

摘要

Standard Galerkin finite-element methods give poor accuracy when applied to second-order elliptic problems with a significant convective term. An upwind finite element was introduced to overcome this difficulty for constant-coefficient problems with zero-source term. This paper extends the use of this type of element to variable-coefficient problems with nonzero-source term by introducing a class of generalised upwind elements, called comparison-upwind finite elements. Two elements from this class are presented in detail. In this paper, we obtain nodal error estimates and global L1 and L2 error estimates for both methods. Finally, some numerical results are presented which demonstrate the methods' accuracy.