ABSTRACT
This chapter considers one, two and three dimensional boundary value problems in single and multi variables that are described by self-adjoint differential operators. The self-adjoint differential operators arise in many branches of engineering, science, and mathematical physics. The essential boundary conditions of the BVP must be described or specified in terms of the dofs at the nodes or grid points of the discretization. This chapter considers two dimensional boundary value problems in single and multiple dependent variables described by self-adjoint differential operators. The element geometry in the physical coordinate space could be a tetrahedron with flat faces and straight edges or it could have curved faces and edges. The element geometry could also consist of a hexahedron with curved faces and edges or flat faces and straight line edges. The element geometry is mapped into a two-unit cube with the origin of the coordinate system at the center of the element.
