Related papers: Analysis for Implicit and Implicit-Explicit ADER a…
In [1] is proposed a simplified DeC method, that, when combined with the residual distribution (RD) framework, allows to construct a high order, explicit FE scheme with continuous approximation avoiding the inversion of the mass matrix for…
We propose a new method that extends conservative explicit multirate methods to implicit explicit-multirate methods. We develop extensions of order one and two with different stability properties on the implicit side. The method is suitable…
In this note, we connect two different topics from linear algebra and numerical analysis: hypocoercivity of semi-dissipative matrices and strong stability for explicit Runge--Kutta schemes. Linear autonomous ODE systems with a non-coercive…
We present a parametric family of semi-implicit second order accurate numerical methods for non-conservative and conservative advection equation for which the numerical solutions can be obtained in a fixed number of forward and backward…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
A growing body of literature has been leveraging techniques of machine learning (ML) to build novel approaches to approximating the solutions to partial differential equations. Noticeably absent from the literature is a systematic…
This paper is devoted to examining the stability of Runge-Kutta methods for solving nonlinear Volterra delay-integro-differential-algebraic equations (DIDAEs) with constant delay. Hybrid numerical schemes combining Runge-Kutta methods and…
We introduce an automatic variationally stable analysis (AVS) for finite element (FE) computations of scalar-valued convection-diffusion equations with non-constant and highly oscillatory coefficients. In the spirit of least squares FE…
Analysis of an interface stabilised finite element method for the scalar advection-diffusion-reaction equation is presented. The method inherits attractive properties of both continuous and discontinuous Galerkin methods, namely the same…
Semi-implicit spectral deferred correction (SDC) methods provide a systematic approach to construct time integration methods of arbitrarily high order for nonlinear evolution equations including conservation laws. They converge towards $A$-…
In this master thesis we have compared different second order stabilized explicit Runge-Kutta methods when applied to the incompressible Navier-Stokes equations by means of a projection method and a differential algebraic approach. We…
The framework of inner product norm preserving relaxation Runge-Kutta methods (David I. Ketcheson, \emph{Relaxation Runge-Kutta Methods: Conservation and Stability for Inner-Product Norms}, SIAM Journal on Numerical Analysis, 2019) is…
The following work presents a generalized (extended) finite element formulation for the advection-diffusion equation. Using enrichment functions that represent the exponential nature of the exact solution, smooth numerical solutions are…
This paper addresses the derivation of generic and tractable sufficient conditions ensuring the stability of a coupled system composed of a reaction-diffusion partial differential equation (PDE) and a finite-dimensional linear time…
We construct, analyse and assess various schemes of second order of accuracy in space and time for model advection-diffusion-reaction differential equations. The constructed schemes are meant to be of practical use in solving industrial…
In this paper, Runge-Kutta-Gegenbauer (RKG) stability polynomials of arbitrarily high order of accuracy are introduced in closed form. The stability domain of RKG polynomials extends in the the real direction with the square of polynomial…
In this paper we analyze a fully discrete numerical scheme for solving a parabolic PDE on a moving surface. The method is based on a diffuse interface approach that involves a level set description of the moving surface. Under suitable…
This paper introduces a novel method for numerically stabilizing sequential continuous adjoint flow solvers utilizing an elliptic relaxation strategy. The proposed approach is formulated as a Partial Differential Equation (PDE) containing a…
A discretization scheme is introduced for a set of convection-diffusion equations with a non-linear reaction term, where the convection velocity is constant for each reactant. This constancy allows a transformation to new spatial variables,…
This paper deals with stability of classical Runge-Kutta collocation methods. When such methods are embedded in linearly implicit methods as developed in [12] and used in [13] for the time integration of nonlinear evolution PDEs, the…