Yamamoto's principle and its applications to precise finite element error analysis.
The paper is concerned with boundary value problems of linear second-order ordinary differential equations boundary value problems with non-coercive principal part, and with linear spline (finite element) methods for their approximation. The main goal is to derive error bounds similar to those known for coercive problems. Here, the essential work consists in obtaining such bounds for the auxiliary problem where the non-principal part is set to zero. For this problem, the Green function is known in closed form; this enables a precise comparison between the inverses of the continuous (differential) and the discrete (finite element) operator, and thus, the desired error bounds. By a compactness argument, the non-principal part is also taken into account, Finally, error bounds for the derivative at the nodal points are derived.
scientific article; zbMATH DE number 1912290