Adaptive mesh refinement in boundary value problems for linear ODE systems
A class of boundary value problems for symmetric systems of 2nd order linear ordinary differential equations (ODEs) is considered. For finding its approximate solution the author constructs a variant of the finite element method based on adaptive mesh refinement with piecewise-linear basis functions. The method does not require any information on the solution singularities and allows to start the computation with a mesh containing only one inner node. The advantage of this approach in comparison with the uniform mesh refinement is that the number of nodes and the computation time can be essentially reduced.
scientific article; zbMATH DE number 1818140
scientific article