An ε-uniform finite element method for singularly perturbed two-point boundary value problems

摘要: This work develops an e-uniform finite element method for singularly perturbed two-point boundary value problems. A surprising and remarkable observation is illustrated: By inserting one node arbitrarily in any element, the new solution always intersects with original at fixed points, errors those points converge same rate as regular problems (without layers). Using this fact, effective approximation out of layer proposed by adding point only that contains layer. The thickness need not be known a priori. Numerical results are carried compared to Shishkin mesh demonstration purpose.