[图书][B] Finite elements III: first-order and time-dependent PDEs
A Ern, JL Guermond - 2021 - books.google.com
This book is the third volume of a three-part textbook suitable for graduate coursework,
professional engineering and academic research. It is also appropriate for graduate flipped …
professional engineering and academic research. It is also appropriate for graduate flipped …
Well-posedness of hp-version discontinuous Galerkin methods for fractional diffusion wave equations
K Mustapha, D Schötzau - IMA Journal of Numerical Analysis, 2014 - ieeexplore.ieee.org
We establish the well-posedness of an hp-version time-stepping discontinuous Galerkin
method for the numerical solution of fractional superdiffusion evolution problems. In …
method for the numerical solution of fractional superdiffusion evolution problems. In …
An - Version of the Continuous Petrov--Galerkin Finite Element Method for Volterra Integro-Differential Equations with Smooth and Nonsmooth Kernels
We present an hp version of the continuous Petrov--Galerkin (CPG) finite element method
for linear Volterra integro-differential equations with smooth and nonsmooth kernels. We …
for linear Volterra integro-differential equations with smooth and nonsmooth kernels. We …
A multistep Legendre--Gauss spectral collocation method for nonlinear Volterra integral equations
We introduce a multistep Legendre--Gauss spectral collocation method for the nonlinear
Volterra integral equations of the second kind. This method is easy to implement and …
Volterra integral equations of the second kind. This method is easy to implement and …
An hp-version of the discontinuous Galerkin time-stepping method for Volterra integral equations with weakly singular kernels
L Wang, H Tian, L Yi - Applied Numerical Mathematics, 2021 - Elsevier
We develop and analyze an hp-version of the discontinuous Galerkin time-stepping method
for linear Volterra integral equations with weakly singular kernels. We derive a priori error …
for linear Volterra integral equations with weakly singular kernels. We derive a priori error …
A posteriori error estimation for hp-version time-stepping methods for parabolic partial differential equations
D Schötzau, TP Wihler - Numerische Mathematik, 2010 - Springer
The aim of this paper is to develop an hp-version a posteriori error analysis for the time
discretization of parabolic problems by the continuous Galerkin (cG) and the discontinuous …
discretization of parabolic problems by the continuous Galerkin (cG) and the discontinuous …
Superconvergent postprocessing of the continuous Galerkin time stepping method for nonlinear initial value problems with application to parabolic problems
M Zhang, L Yi - Journal of Scientific Computing, 2023 - Springer
We introduce and analyze a very simple but efficient postprocessing technique for improving
the accuracy of the continuous Galerkin (CG) time stepping method for nonlinear first-order …
the accuracy of the continuous Galerkin (CG) time stepping method for nonlinear first-order …
[PDF][PDF] Postprocessing techniques of high-order Galerkin approximations to nonlinear second-order initial value problems with applications to wave equations …
MZ Zhang, LJ Yi - Comput. Phys., 2024 - researchgate.net
The aim of this paper is to propose and analyze two postprocessing techniques for
improving the accuracy of the C1-and C0-continuous Galerkin (CG) time stepping methods …
improving the accuracy of the C1-and C0-continuous Galerkin (CG) time stepping methods …
hp-version C1-continuous Petrov–Galerkin method for nonlinear second-order initial value problems with application to wave equations
L Wang, M Zhang, H Tian, L Yi - IMA Journal of Numerical …, 2024 - academic.oup.com
We introduce and analyze an-version-continuous Petrov–Galerkin (CPG) method for
nonlinear initial value problems of second-order ordinary differential equations. We derive a …
nonlinear initial value problems of second-order ordinary differential equations. We derive a …
An L∞-error estimate for the hp version continuous Petrov-Galerkin method for nonlinear initial value problems
L Yi - East Asian Journal on Applied Mathematics, 2015 - cambridge.org
The hp version of the continuous Petrov-Galerkin time stepping method is analyzed for
nonlinear initial value problems. An L∞-error bound explicit with respect to the local …
nonlinear initial value problems. An L∞-error bound explicit with respect to the local …