We consider linear and semilinear parabolic problems posed in high-contrast multiscale media in two dimensions. The presence of high-contrast multiscale media adversely affects the accuracy, stability, and overall efficiency ...

Residual minimization is a widely used technique for solving Partial Differential Equations in variational form. It minimizes the dual norm of the residual, which naturally yields a saddle-point (min–max) problem over the ...

In this article, we propose an algorithm for approximating the action of  $\varphi$-functions of matrices against vectors, which is a key operation in exponential time integrators. In particular, we consider matrices with ...

In this article, we present a general methodology to combine the Discontinuous Petrov-Galerkin (DPG) method in space and time in the context of methods of lines for transient advection-reaction problems. We  rst introduce ...

Exponential time integrators are well-established discretization methods for time semilinear systems of ordinary differential equations. These methods use (Formula presented.) functions, which are matrix functions related ...

In this article, we introduce an error representation function to perform adaptivity in time of the recently developed time-marching Discontinuous Petrov–Galerkin (DPG) scheme. We first provide an analytical expression for ...

We study both conforming and non-conforming versions of the practical DPG method for the convection-reaction problem. We determine that the most common approach for DPG stability analysis - construction of a local Fortin ...

The Discontinuous Petrov-Galerkin (DPG) method and the exponential integrators are two well established numerical methods for solving Partial Di fferential Equations (PDEs) and sti ff systems of Ordinary Di fferential ...

The Discontinuous Petrov-Galerkin (DPG) method is a widely employed discretization method for Partial Di fferential Equations (PDEs). In a recent work, we applied the DPG method with optimal test functions for the time ...

Goal-Oriented Adaptivity (GOA) is a powerful tool to accurately approximate physically relevant features of the solution of Partial Differential Equations (PDEs). It delivers optimal grids to solve challenging engineering ...