We develop the a posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finiteelement methods for a class of second-order quasi-linear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh dependent) energy norm. The bounds are explicit in the local mesh size and the local polynomial degree of the...

A novel spectral-element approach for the eikonal equation is presented based on the work of Tucker et al. This approach is readily implemented in standard finiteelement flow solvers developed for the Navier-Stokes equations. Results are presented for distance function (level set) for three planar configurations: circular cylinder, NACA 0012 airfoil, and T106 airfoil. Results demonstrate that t...

Following the pioneering work of Keller and others in the 1970s and ’80s, numerical techniques for solving non-linear systems of equations that exhibit bifurcations have been developed to the point where they can potentially be applied to a wide range of problems arising in continuum mechanics. The central idea is to augment the discretised governing equations with one or more conditions so tha...

The experimental determination of fracture mechanical properties of interface cracks is a substantial task for the design for reliability of electronic packages. As interface cracks are dominated by a mode mix between tension and shear mode (crack driving modes I and II) a mixed mode bending method was developed to adjust the ratio of the two modes (mode mixity). For a correct extraction of an ...

Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finiteelement ...

Introduction. The development of new dental implants in the context booming domestic industry makes it possible to find alternative options treatment clinically difficult situations, select necessary individual solution during implant surgery and consequently perform an error-free manner achieve desired results. a is multistep process, characteristics material its biophysical must be studied de...

In this work, we investigated the effect of pitch distance on statistical variation and morphology extrusion in Cu through-silicon vias (TSVs) underlying mechanisms. Extrusion statistics were obtained from TSV samples with two different distances. A notable increase magnitude was observed smaller pitch, yet spread largely unaffected. The morphologies extruded characterized categorized, a finite...

Singlet oxygen ( 1 O2) is the major cytotoxic agent during photodynamic therapy (PDT). A previously developed model that incorporates the diffusion equation for the light transport in tissue and the macroscopic kinetic equations for the generation of the singlet oxygen, can be used to numerically calculate the distance-dependent reacted 1 O2 using finiteelement method (FEM). The formula of reac...

A modern multi-purpose baroclinic circulation model (SELFE) has been recently extended to include the ability to simulate tsunami propagation and inundation. The core model is based on the 3-D nonlinear shallow-water wave (NSW) equations, which are solved on unstructured grids, using the finiteelement method. A semi-implicit method is used to solve all equations to enhance numerical stability, ...

A highly accurate numerical scheme is presented for the Serre system of partial differential equations, which models the propagation of dispersive shallow water waves in the fully-nonlinear regime. The fully-discrete scheme utilizes the Galerkin / finiteelement method based on smooth periodic splines in space, and an explicit fourth-order Runge-Kutta method in time. Computations compared with e...