8 papers · 1 filter
Conservative Finite Element Methods for Kirchhoff-Type Equations
Benjamin Dörich, Felix Krumbiegel, Jemal Rogava +2
We construct and analyse a fully discrete scheme for a Kirchhoff-type nonlinear integro-differential equation in two spatial dimensions with time-dependent coefficients. The scheme…
Conservative Three-Layer Schemes for Kirchhoff-Type Equations
Felix Krumbiegel, Jemal Rogava, Andreas Rupp +1
We study a Kirchhoff-type nonlinear integro-differential equation in two spatial dimensions whose coefficients are allowed to depend on time, and we construct conservative discreti…
A Convergent Hybridizable Discontinuous Galerkin Method for Einstein--Scalar Equations
Mukul Dwivedi, Andreas Rupp
We propose and analyze a hybridized discontinuous Galerkin (HDG) method for the spherically symmetric Einstein--scalar system in Bondi gauge. After rewriting the model as a local f…
A Galerkin Finite Element Method for the Fractional Calderón Problem
Mukul Dwivedi, Jesse Railo, Andreas Rupp
We study a numerical reconstruction strategy for the potential in the fractional Calderón problem from a single partial exterior measurement. The forward model is the fractional Sc…
A hybridizable discontinuous Galerkin method for the Ostrovsky equation
Mukul Dwivedi, Andreas Rupp
This paper develops the hybridizable discontinuous Galerkin (HDG) method for the Ostrovsky equation, a nonlinear dispersive wave equation featuring both third-order dispersion and…
A Hybridizable Discontinuous Galerkin Method for the non--local Camassa--Holm--Kadomtsev--Petviashvili equation
Mukul Dwivedi, Ruben Gutendorf, Andreas Rupp
This paper develops a hybridizable discontinuous Galerkin method for the two-dimensional Camassa--Holm--Kadomtsev--Petviashvili equation. The method employs Cartesian meshes with t…
A numerical method for the fractional Zakharov-Kuznetsov equation
Mukul Dwivedi, Andreas Rupp
This paper develops a fully discrete Fourier spectral Galerkin (FSG) method for the fractional Zakharov--Kuznetsov (fZK) equation posed on a two-dimensional periodic domain. The eq…
A convergent Fourier spectral Galerkin method for the fractional Camassa-Holm equation
Mukul Dwivedi, Andreas Rupp
We analyze a Fourier spectral Galerkin method for the fractional Camassa-Holm (fCH) equation involving a fractional Laplacian of exponent with periodic boundary condit…