4 papers
Certified neural approximations for parabolic obstacle problems
Davood Damircheli
Residual-trained neural surrogates carry no error guarantee, a limitation for free-boundary problems such as phase change and contact. We derive guaranteed error bounds for neural…
A space-time finite element method for parabolic obstacle problems
José Joaquín Carvajal, Davood Damircheli, Thomas Führer +2
We propose and analyze a general framework for space-time finite element methods that is based on least-squares finite element methods for solving a first-order reformulation of th…
On a Stable Method for Option Pricing: Discontinuous Petrov-Galerkin Method for Option Pricing and Sensitivity Analysis
Davood Damircheli
The discontinuous Petrov Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan introduced in their first paper has been widely used for problems in computational mechanics. In…
Recovered-Coefficient Discontinuous Galerkin Approximation of an Averaged-State Credit-Rating Migration PDE
Davood Damircheli
We develop and analyze a discontinuous Galerkin (DG) method for an averaged-state regularization of a credit-rating migration equation, in which the volatility switch is smoothed a…