An easy treatment of hanging nodes in hp-finite elements

Abstract We present an easy treatment of (multi-level) hanging nodes in hp -finite elements in two dimensions. Its simplicity is due to the fact that the connectivity matrices can directly be computed in a row-wise fashion. This is achieved by treating a global degree of freedom as a local degree of freedom on each element in an appropriate union of elements. This forms a type of support which is larger than the one used in the conventional approach and generalizes the recently presented multi-level hp -method. Our method requires the global degrees of freedom to be derived from tensor-product shape functions. It supports refinements of general quadrilaterals and curvilinear elements since refinements are performed on the reference element. While the method can be applied most efficiently if the subdivision leads to a paraxial subset of the reference element, also non-paraxial refinements are supported. Numerical experiments compare the new approach with respect to accuracy and the conditioning of the resulting linear system. We conclude that this new approach achieves nearly the same properties as the conventional approach in all investigated examples and provides an excellent trade-off between implementational complexity and solvability.