In numerical time-integration with implicit-explicit (IMEX) methods, a within-step adaptable
decomposition called residual balanced (RB) decomposition is introduced. This new …

Classical a posteriori error analysis for differential equations quantifies the error in a
Quantity of Interest which is represented as a bounded linear functional of the solution. In …

Abstract The Poisson‐Boltzmann equation is a widely used model to study electrostatics in
molecular solvation. Its numerical solution using a boundary integral formulation requires a …

We construct a space‐time parallel method for solving parabolic partial differential equations
by coupling the parareal algorithm in time with overlap** domain decomposition in space …

Abstract Domain decomposition methods are widely used for the numerical solution of
partial differential equations on high performance computers. We develop an adjoint-based …

We develop an a posteriori error analysis for a numerical estimate of the time at which a
functional of the solution to a partial differential equation (PDE) first achieves a threshold …

The spectral deferred correction method is a variant of the deferred correction method for
solving ordinary differential equations. A benefit of this method is that is uses low order …

This thesis derives two Uncertainty Quantification (UQ) methods for differential equations
that depend on random parameters:(i) error bounds for a computed cumulative distribution …

Adjoint based a posteriori error analysis is a technique to produce exact error repre-
sentations for quantities of interests that are functions of the solution of systems of partial …