Now showing items 1-4 of 4
A space-time DPG method for the wave equation in multiple dimensions
A space-time discontinuous Petrov–Galerkin (DPG) method for the linear wave equation is presented. This method is based on a weak formulation that uses a broken graph space. The well-posedness of this formulation is ...
Asymptotic Models for the Electric Potential across a Highly Conductive Casing
We analyze a configuration that involves a steel-cased borehole, where the casing that covers the borehole is considered as a highly conductive thin layer. We develop an asymptotic method for deriving reduced problems ...
A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements
In some geological formations, borehole resistivity measurements can be simulated using a sequence of 1D models. By considering a 1D layered media, we can reduce the dimensionality of the problem from 3D to 1.5D via a ...
Discrete maximum principles for nonlinear parabolic PDE systems
Discrete maximum principles (DMPs) are established for finite element approximations of systems of nonlinear parabolic partial differential equations with mixed boundary and interface conditions. The results are based on ...