Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure I

Preface.- Introduction.-An Introduction to the p- and hp-versions of the Finite Element Method.-Eigen-pairs Computation for Two-Dimensional Heat Conduction Singularities.-Computation of GFIFs for Two-Dimensional Heat Conduction Problems.-Eigen-pairs for two-dimensional elasticity.-Computing Generalized Stress Intensity Factors.-Thermal Generalized Stress Intensity Factors in 2-D Domains.-Failure Criteria for Brittle Elastic Materials.-Thermo-Mechanical Failure Criterion at the Micron Scale in Electronic Devices.-Singular solutions of the heat conduction equation in polyhedra domains.-Computation of the Edge Flux Intensity Functions associated with polyhedra domains.-Vertex singularities associated with conical points for the 3-D Laplace equation.-Edge eigen-pairs and ESIFs of 3-D elastic problems.-Summary and Open Questions.