"uuid","repository link","title","author","contributor","publication year","abstract","subject topic","language","publication type","publisher","isbn","issn","patent","patent status","bibliographic note","access restriction","embargo date","faculty","department","research group","programme","project","coordinates"
"uuid:9f1b5718-b4a3-4d9f-8e0f-46bd75e5cd48","http://resolver.tudelft.nl/uuid:9f1b5718-b4a3-4d9f-8e0f-46bd75e5cd48","Spectral element method for parabolic interface problems","Khan, Arbaz (University of Manchester); Upadhyay, Chandra Shekhar (Indian Institute of Technology Kanpur); Gerritsma, M.I. (TU Delft Aerodynamics)","","2018","In this paper, an h∕p spectral element method with least-square formulation for parabolic interface problem will be presented. The regularity result of the parabolic interface problem is proven for non-homogeneous interface data. The differentiability estimates and the main stability estimate theorem, using non-conforming spectral element functions, are proven. Error estimates are derived for h and p versions of the proposed method. Specific numerical examples are given to validate the theory.","Least-squares method; Linear parabolic interface problems; Nonconforming; Sobolev spaces of different orders in space and time; Spectral element method","en","journal article","","","","","","","","2020-04-07","","","Aerodynamics","","",""
"uuid:d77c1eba-e97a-4d76-a4e0-d6aad5f0d6cb","http://resolver.tudelft.nl/uuid:d77c1eba-e97a-4d76-a4e0-d6aad5f0d6cb","Mimetic Least-Squares: A Least-Squares Formulation with Exact Conservation Properties","Bochev, P.; Gerritsma, M.I.","","2014","We present a spectral mimetic least-squares method which is fully conservative and decouples the primal and dual variables.","least-squares; mimetic methods; conservation; spectral methods","en","conference paper","CIMNE","","","","","","","","Aerospace Engineering","Aerodynamics, Wind Energy & Propulsion","","","",""
"uuid:7b6dd1e0-1635-449a-ac2e-c2eaa232eb48","http://resolver.tudelft.nl/uuid:7b6dd1e0-1635-449a-ac2e-c2eaa232eb48","The geometric basis of mimetic spectral approximations","Gerritsma, M.I.","Hiemstra, R. (contributor); Kreeft, J.J. (contributor); Palha, A. (contributor); Rebelo, P. (contributor)","2012","","","en","lecture notes","","","","","","","","","Aerospace Engineering","Aerodynamics, Wind Energy & Propulsion","","","",""
"uuid:50d894cf-88fe-4ecb-87ee-e1f1128b7763","http://resolver.tudelft.nl/uuid:50d894cf-88fe-4ecb-87ee-e1f1128b7763","Least-squares spectral element methods for compressible flows","Gerritsma, M.I.","","2008","","","en","conference paper","University of Pretoria","","","","","","","","Aerospace Engineering","","","","",""
"uuid:badf6b35-3d75-4234-8cd2-361f9b62116f","http://resolver.tudelft.nl/uuid:badf6b35-3d75-4234-8cd2-361f9b62116f","Time-Dependent Polynomial Chaos","Gerritsma, M.I.; Vos, P.; Van der Steen, J.B.","","2008","","uncertainty; stochastic ODE; Kraichnan-Orszag problem polynomial chaos; long-term integration","en","conference paper","European Society of Computational Methods in Sciences and Engineering","","","","","","","","Aerospace Engineering","","","","",""
"uuid:a0c368e2-8cc2-40c8-98cb-a6916ffc7589","http://resolver.tudelft.nl/uuid:a0c368e2-8cc2-40c8-98cb-a6916ffc7589","Constrained least-squares methods for partial differential equations","De Maerschalck, B.; Gerritsma, M.I.","","2006","Least-squares methods for partial differential equations are based on a norm-equivalence between the error norm and the residual norm. The resulting algebraic system of equations, which is symmetric positive definite, can also be obtained by solving a weighted collocation scheme using least-squares to solve the resulting algebraic equations. Furthermore, least-squares allows to ad extra constraints to the system. In the present work the entropy is added as an extra inequality constraint to ensure only physical solutions for the one-dimensional inviscid Burgers equation are obtained.","least-squares; spectral elements; space-time; entropy condition","en","conference paper","Delft University of Technology; European Community on Computational Methods in Applied Sciences (ECCOMAS)","","","","","","","","Aerospace Engineering","","","","",""
"uuid:df762acc-025c-4af4-a4c7-0c211ed17639","http://resolver.tudelft.nl/uuid:df762acc-025c-4af4-a4c7-0c211ed17639","Constrained least-squares methods for partial differential equations","De Maerschalck, B.; Gerritsma, M.I.","","2006","Least-squares methods for partial differential equations are based on a norm-equivalence between the error norm and the residual norm. The resulting algebraic system of equations, which is symmetric positive definite, can also be obtained by solving a weighted collocation scheme using least-squares to solve the resulting algebraic equations. Furthermore, least-squares allows to ad extra constraints to the system. In the present work the entropy is added as an extra inequality constraint to ensure only physical solutions for the one-dimensional inviscid Burgers equation are obtained.","least-squares; spectral elements; space-time; entropy condition","en","conference paper","","","","","","","","","","","","","",""
"uuid:c2b46495-4063-4249-a4d5-8b8d38a4af00","http://resolver.tudelft.nl/uuid:c2b46495-4063-4249-a4d5-8b8d38a4af00","Least-squares spectral element method with implicit time integration for the inviscid Burgers equation","Oldenziel, G.; Gerritsma, M.I.","","2006","This paper describes the use of the Least-Squares Spectral Element Method for non-linear hyperbolic equations. The one-dimensional inviscid Burgers equation is specifically subject of investigation. A second order backward difference method is used for time stepping. The behaviour of this formulation is examined by application to a testcase where a moving shock develops. For this testcase an hp-convergence study is performed.","Least-Squares Spectral Element Methods; hyperbolic equations; hp-convergence","en","conference paper","","","","","","","","","","","","","",""
"uuid:5a2ae89d-961a-4251-bc03-c642a2d6d6e4","http://resolver.tudelft.nl/uuid:5a2ae89d-961a-4251-bc03-c642a2d6d6e4","Aspects of goal-oriented model-error estimation in convection-diffusion problems","Cnossen, J.M.; Bijl, H.; Gerritsma, M.I.; Koren, B.","","2006","For goal-oriented model adaptation a model-error estimator is required to drive the adaptation process. In recent years publications have appeared on the dual-weighted residual (DWR) method in the application of model-error estimation in output functionals. In this paper we study the application of the DWR method for convection-diffusion problems where hierarchical models are of different type. Omitting the diffusion operator often results in a singular perturbation problem considering the model residual in the limit of vanishing diffusion. This is caused by the change of mathematical type of the model equations and therefore the applied boundary conditions. In this work we show how a model error estimator is developed for steady and unsteady convection-diffusion problems. It is found that a weak formulation and weakly imposing boundary and initial conditions leads to a dual-weighted model-error estimator that also incorporates boundary residuals.","model error; hierarchical modelling; goal-oriented error estimation; dualweighted residual method; convection-diffusion problems","en","conference paper","Delft University of Technology; European Community on Computational Methods in Applied Sciences (ECCOMAS)","","","","","","","","Aerospace Engineering","","","","",""
"uuid:74a8a8be-6cf7-4a2d-bd8d-1874597ac2e1","http://resolver.tudelft.nl/uuid:74a8a8be-6cf7-4a2d-bd8d-1874597ac2e1","Least-squares spectral element method with implicit time integration for the inviscid Burgers equation","Oldenziel, G.; Gerritsma, M.I.","","2006","This paper describes the use of the Least-Squares Spectral Element Method for non-linear hyperbolic equations. The one-dimensional inviscid Burgers equation is specifically subject of investigation. A second order backward difference method is used for time stepping. The behaviour of this formulation is examined by application to a testcase where a moving shock develops. For this testcase an hp-convergence study is performed.","Least-Squares Spectral Element Methods; hyperbolic equations; hp-convergence","en","conference paper","Delft University of Technology; European Community on Computational Methods in Applied Sciences (ECCOMAS)","","","","","","","","Aerospace Engineering","","","","",""
"uuid:d4d2202c-73c2-4028-b8b7-425f2029fdbe","http://resolver.tudelft.nl/uuid:d4d2202c-73c2-4028-b8b7-425f2029fdbe","Aspects of goal-oriented model-error estimation in convection-diffusion problems","Cnossen, J.M.; Bijl, H.; Gerritsma, M.I.; Koren, B.","","2006","For goal-oriented model adaptation a model-error estimator is required to drive the adaptation process. In recent years publications have appeared on the dual-weighted residual (DWR) method in the application of model-error estimation in output functionals. In this paper we study the application of the DWR method for convection-diffusion problems where hierarchical models are of different type. Omitting the diffusion operator often results in a singular perturbation problem considering the model residual in the limit of vanishing diffusion. This is caused by the change of mathematical type of the model equations and therefore the applied boundary conditions. In this work we show how a model error estimator is developed for steady and unsteady convection-diffusion problems. It is found that a weak formulation and weakly imposing boundary and initial conditions leads to a dual-weighted model-error estimator that also incorporates boundary residuals.","model error; hierarchical modelling; goal-oriented error estimation; dualweighted residual method; convection-diffusion problems","en","conference paper","","","","","","","","","","","","","",""
"uuid:6d6cebba-ddea-46e4-b0bf-71650484450b","http://resolver.tudelft.nl/uuid:6d6cebba-ddea-46e4-b0bf-71650484450b","Error convergence of the Least-Squares Spectral Element formulation of the linear advection-reaction equation","Van Dalen, W.R.; Gerritsma, M.I.","","2006","This paper discusses the use of the Least-Squares Spectral Element Method in solving the linear, 1-dimensional advection-reaction equation. Well-posedness of the Least-Squares formulation will be derived. The formulation and its results will be compared to the standard Galerkin Spectral Element Method.","least-squares formulation; spectral methods; Galerkin formulation; advectionreaction equation","en","conference paper","Delft University of Technology; European Community on Computational Methods in Applied Sciences (ECCOMAS)","","","","","","","","Aerospace Engineering","","","","",""
"uuid:0bfb0cdb-7fc8-45ca-8e80-0aa2930c2396","http://resolver.tudelft.nl/uuid:0bfb0cdb-7fc8-45ca-8e80-0aa2930c2396","Application of Least-Squares Spectral Element Methods to Polynomial Chaos","Vos, P.E.J.; Gerritsma, M.I.","","2006","This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conventional Galerkin projection.","least squares; spectral elements; polynomial chaos; stochastic differential equations","en","conference paper","","","","","","","","","","","","","",""
"uuid:06ea1c34-025d-4e7e-b489-eb42a9dc29de","http://resolver.tudelft.nl/uuid:06ea1c34-025d-4e7e-b489-eb42a9dc29de","Error convergence of the Least-Squares Spectral Element formulation of the linear advection-reaction equation","Van Dalen, W.R.; Gerritsma, M.I.","","2006","This paper discusses the use of the Least-Squares Spectral Element Method in solving the linear, 1-dimensional advection-reaction equation. Well-posedness of the Least-Squares formulation will be derived. The formulation and its results will be compared to the standard Galerkin Spectral Element Method.","least-squares formulation; spectral methods; Galerkin formulation; advectionreaction equation","en","conference paper","","","","","","","","","","","","","",""
"uuid:a5b8033b-f4e1-4100-9e6a-ec9ff697019c","http://resolver.tudelft.nl/uuid:a5b8033b-f4e1-4100-9e6a-ec9ff697019c","Application of Least-Squares Spectral Element Methods to Polynomial Chaos","Vos, P.E.J.; Gerritsma, M.I.","","2006","This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conventional Galerkin projection.","least squares; spectral elements; polynomial chaos; stochastic differential equations","en","conference paper","Delft University of Technology; European Community on Computational Methods in Applied Sciences (ECCOMAS)","","","","","","","","Aerospace Engineering","","","","",""
"uuid:c76a3c86-16d6-42fd-abdc-a5a5b49ec458","http://resolver.tudelft.nl/uuid:c76a3c86-16d6-42fd-abdc-a5a5b49ec458","Time Dependent Flow Simulations using the Least Squares Spectral Element Method with Direct Minimization","Kwakkel, M.; Gerritsma, M.I.","","2006","In this work a new approach to time dependent problems in combination with the Least-Squares Spectral Element Method (LSQSEM) will be discussed. Various time-stepping formulations will be presented. These time-stepping formulations will be compared to the full space-time formulation. It will be shown that time-stepping formulations give accurate results for comparable CPU times. Furthermore is will be shown that a smaller timestep or a higher polynomial degree not always decreases the error norm.","least-squares; spectral elements; time-stepping","en","conference paper","","","","","","","","","","","","","",""
"uuid:795f6c19-2304-4592-8a62-f0d33560db89","http://resolver.tudelft.nl/uuid:795f6c19-2304-4592-8a62-f0d33560db89","Time Dependent Flow Simulations using the Least Squares Spectral Element Method with Direct Minimization","Kwakkel, M.; Gerritsma, M.I.","","2006","In this work a new approach to time dependent problems in combination with the Least-Squares Spectral Element Method (LSQSEM) will be discussed. Various timestepping formulations will be presented. These time-stepping formulations will be compared to the full space-time formulation. It will be shown that time-stepping formulations give accurate results for comparable CPU times. Furthermore is will be shown that a smaller timestep or a higher polynomial degree not always decreases the error norm.","least-squares; spectral elements; time-stepping","en","conference paper","Delft University of Technology; European Community on Computational Methods in Applied Sciences (ECCOMAS)","","","","","","","","Aerospace Engineering","","","","",""