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Error estimates for the fully-discrete Petrov-Galerkin method of a linear parabolic problem
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hp-error analysis of a continuous Petrov–Galerkin time-stepping scheme for linear parabolic equations
New regularity results and finite element error estimates for a class of parabolic optimal control problems with pointwise state constraints
Constantin Christof, Boris Vexler, G. Buttazzo, et al. ESAIM: Control, Optimisation and Calculus of Variations 27 4 (2021) https://doi.org/10.1051/cocv/2020059
A posteriori error bounds for fully-discrete hp-discontinuous Galerkin timestepping methods for parabolic problems
Numerical analysis of sparse initial data identification for parabolic problems
Dmitriy Leykekhman, Boris Vexler and Daniel Walter ESAIM: Mathematical Modelling and Numerical Analysis 54(4) 1139 (2020) https://doi.org/10.1051/m2an/2019083
Weak Galerkin method with implicit θ-schemes for second-order parabolic problems
Numerical Study of SUPG and LPS Methods Combined with Higher Order Variational Time Discretization Schemes Applied to Time-Dependent Linear Convection–Diffusion–Reaction Equations
Multiple Shooting and Time Domain Decomposition Methods
Tuğba Akman and Bülent Karasözen Contributions in Mathematical and Computational Sciences, Multiple Shooting and Time Domain Decomposition Methods 9 233 (2015) https://doi.org/10.1007/978-3-319-23321-5_9
A Priori Error Estimates for a Finite Element Discretization of Parabolic Optimization Problems with Pointwise Constraints in Time on Mean Values of the Gradient of the State
Francesco Ludovici and Winnifried Wollner SIAM Journal on Control and Optimization 53(2) 745 (2015) https://doi.org/10.1137/140961778
Higher order continuous Galerkin−Petrov time stepping schemes for transient convection-diffusion-reaction equations
Domain Decomposition Methods in Science and Engineering XXI
Thi-Thao-Phuong Hoang, Jérôme Jaffré, Caroline Japhet, Michel Kern and Jean Roberts Lecture Notes in Computational Science and Engineering, Domain Decomposition Methods in Science and Engineering XXI 98 295 (2014) https://doi.org/10.1007/978-3-319-05789-7_26
Variational time discretization methods for optimal control problems governed by diffusion–convection–reaction equations
Higher order accurate discontinuous and continuous p‐Galerkin methods for linear elastodynamics
T. Gleim and D. Kuhl ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 93(2-3) 177 (2013) https://doi.org/10.1002/zamm.201200044
Discontinuous Galerkin and multiscale variational schemes for a coupled damped nonlinear system of Schrödinger equations
M. Asadzadeh, D. Rostamy and F. Zabihi Numerical Methods for Partial Differential Equations 29(6) 1912 (2013) https://doi.org/10.1002/num.21782
An efficient and stable finite element solver of higher order in space and time for nonstationary incompressible flow
S. Hussain, F. Schieweck and S. Turek International Journal for Numerical Methods in Fluids 73(11) 927 (2013) https://doi.org/10.1002/fld.3831
Optimal A Priori Error Estimates of Parabolic Optimal Control Problems with Pointwise Control
Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system
Konstantinos Chrysafinos, Sotirios P. Filopoulos and Theodosios K. Papathanasiou ESAIM: Mathematical Modelling and Numerical Analysis 47(1) 281 (2013) https://doi.org/10.1051/m2an/2012028
A priori error estimates for space–time finite element discretization of semilinear parabolic optimal control problems
Constrained Optimization and Optimal Control for Partial Differential Equations
Dominik Meidner and Boris Vexler International Series of Numerical Mathematics, Constrained Optimization and Optimal Control for Partial Differential Equations 160 445 (2012) https://doi.org/10.1007/978-3-0348-0133-1_23
Higher-order accurate implicit time integration schemes for transport problems
Constrained Optimization and Optimal Control for Partial Differential Equations
Dominik Meidner and Boris Vexler International Series of Numerical Mathematics, Constrained Optimization and Optimal Control for Partial Differential Equations 160 319 (2012) https://doi.org/10.1007/978-3-0348-0133-1_18
Optimized Schwarz Waveform Relaxation and Discontinuous Galerkin Time Stepping for Heterogeneous Problems
Laurence Halpern, Caroline Japhet and Jérémie Szeftel SIAM Journal on Numerical Analysis 50(5) 2588 (2012) https://doi.org/10.1137/120865033
Symmetric error estimates for discontinuous Galerkin
approximations for an optimal control problem associated to
semilinear parabolic PDE's
Output error estimation strategies for discontinuous Galerkin discretizations of unsteady convection‐dominated flows
Krzysztof J. Fidkowski International Journal for Numerical Methods in Engineering 88(12) 1297 (2011) https://doi.org/10.1002/nme.3224
An $hp$-Version Discontinuous Galerkin Method for Integro-Differential Equations of Parabolic Type
K. Mustapha, H. Brunner, H. Mustapha and D. Schötzau SIAM Journal on Numerical Analysis 49(4) 1369 (2011) https://doi.org/10.1137/100797114
Domain Decomposition Methods in Science and Engineering XIX
Laurence Halpern, Caroline Japhet* and Jérémie Szeftel Lecture Notes in Computational Science and Engineering, Domain Decomposition Methods in Science and Engineering XIX 78 75 (2011) https://doi.org/10.1007/978-3-642-11304-8_7
Time discretisation of monotone nonlinear evolution problems by the discontinuous Galerkin method
Domain Decomposition Methods in Science and Engineering XIX
Laurence Halpern, Caroline Japhet* and Jérémie Szeftel* Lecture Notes in Computational Science and Engineering, Domain Decomposition Methods in Science and Engineering XIX 78 133 (2011) https://doi.org/10.1007/978-3-642-11304-8_13
Piecewise-linear, discontinuous Galerkin method for a fractional diffusion equation
Vibration analysis for elastic multi‐beam structures by the C0‐continuous time‐stepping finite element method
Junjiang Lai, Jianguo Huang and Zhongci Shi International Journal for Numerical Methods in Biomedical Engineering 26(2) 205 (2010) https://doi.org/10.1002/cnm.1143
Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's