# NA & SC Preprint Series

**Numerical Analysis & Scientific Computing Preprint Series Department of Mathematics, University of Houston**

**2022**

- R.H.W. Hoppe, B. R. Pahari, J. J. Winkle, Numerical Simulation of the Formation of Spherulites in Polycrystalline Binary Mixtures, No. 67 - August 2022
- D. Braess, R.H.W. Hoppe, C. Linsenmann, A Two-energies Principle for the Biharmonic Equation and an a Posteriori Error Estimator for an Interior Penalty Discontinuous Galerkin Approximations, No. 66 - August 2022

**2019**

- C. Bhandari, R.H.W. Hoppe, R. Kumar, A C
^{0}interior Penalty Discontinuous Galerkin Method for Fourth Order Total Variation Flow. II: Existence and Uniqueness, No. 65 - January 2019 - C. Bhandari, R.H.W. Hoppe, R. Kumar, A C
^{0}Interior Penalty Discontinuous Galerkin Method for Fourth Order Total Variation Flow. I: Derivation of the Method and Numerical Results, No. 64 - January 2019 - R.H.W. Hoppe, J.J. Winkle, Numerical Solution of a Phase Field Model for Polycrystallization Processes in Binary Mixtures, No. 63 - January 2019
- R.H.W. Hoppe, J.J. Winkle, A Splitting Scheme for the Numerical Solution of the Kobayashi-Warren-Carter System, No. 62 - January 2019

**2017**

- Y. Kuznetsov, New Homogenization Method for Diffusion Equations, No. 61 - December 2017
- A. Danilov, A. Lozovskiy, M.A. Olshanskii, Yu. V. Vassilevski, A Finite Element Method for The Navier-Strokes Equations in Moving Domain with Application to Hemodynamics of the Left Ventricle, No. 60 - May 2017
- Y. Wang, A. Quaini, S. Čanić , A Higher-order Discontinuous Galerkin/arbitrary Lagrangian Eulerian Partitioned Approach to Solving Fluid-structure Interaction Problems with Incompressible, Viscous Fluids and Elastic Structures, No. 59 - April 2017
- Y. Gorb, D. Kurzanova, Y. Kuznetsov, A Robust Preconditioner for High-Contrast Problems, No. 58 - January 2017

**2016**

- A. Agrawal and R.H.W. Hoppe, Optimization of Plane Wave Directions In Plane Wave Discontinuous Galerkin Methods For The Helmholtz Equation, No. 57 - September 2016
- R.H.W. Hoppe, and C. Linsenmann, C
^{0}Interior Penalty Discontinuous Galerkin Approximation of A Sixth Order Cahn-Hilliard Equation Modeling Microemulsification Processes, No. 56 - September 2016 - Y. Wang, A. Quaini, S. Čanić, and S.H. Little, 3D Experimental and Computational Analysis of Eccentric Mitral Regurgitant Jets in a Mock Imaging Heart Chamber, No. 55 - August 2016
- G. Pitton, A. Quaini, and G. Rozza, Computational Reduction Strategies for Bifurcations and Stability in Fluid-Dynamics: Applications to Coanda Effect, No. 54 - June 2016
- L. Bertagna, A. Quaini, and L.G. Rebholz, and A. Veneziani, On the Sensitivity To the Filtering Radius In Leray Models of Incompressible FLow, No. 53 - June 2016
- J. Guzmán, and M.A. Olshanskii, Inf-sup Stability of Geometrically Unfitted Stokes Finite Elements, No. 52 - May 2016
- S. Charnyi, T. Heister, M.A. Olshanskii, and L. G. Rebholz, On Conservation Laws of Navier-Stokes Galerkin Discretizations, No. 51 - May 2016
- I. N. Konshin, M.A. Olshanskii, and Yu. V. Vassilevski, An Algebraic Solver For the Oseen Problem With Application to Hemodynamics, No. 50 - May 2016
- I. N. Konshin, M.A. Olshanskii, and Yu. V. Vassilevski, LU Factorizations and ILU Preconditioning for Stabilized Discretizations of Incompressible Navier-Strokes Equations, No. 49 - May, 2016.
- D. Braess, R.H.W. Hoppe, and C. Linsenmann, A Two-energies Principle for the Biharmonic Equation and an a Posteriorierror Estimator for an Interior Penalty Discontinuous Galerkin Approximation, No. 48 - March, 2016.
- D. Forti, M. Bukac, A. Quaini, S. Čanić, and S. Deparis, A Monolithic Approach to Fluid-Composite Structure Interaction, No. 47 - February, 2016.
- T.K. Dobroserdova, M.A. Olshanskii, and S.S. Simakov, Multiscale Coupling of Compliant and Rigid Walls Blood Flow Models, No. 46 - January, 2016.

**2015**

- M.A. Olshanskii, and D. Safin, Numerical Integration Over Implicitly Defined Domains for Higher Order Unfitted Finite Element Methods, No. 45 - November, 2015.
- K.M. Terekhov, K.D. Nikitin, M.A. Olshanskii, and Y.V Vassilevski, A Semi-Largangian Method on Dynamically Adapted Octree Meshes, No. 44 - November, 2015.
- A. Cesmelioglu, H. Lee, A. Quaini, K. Wang, and S.-Y. Yi, Optimization-based Decoupling Algorithms For a Fluid-poroelastic System, No. 43 - November, 2015.
- L. Shi, S. Čanić, A. Quaini, and T.-W. Pan, A Study of Self-Propelled Elastic Cylindrical Micro-swimmers Using Modeling and Computation, No. 42 - October, 2015.
- O. Boyarkin, R.H.W. Hoppe, and C. Linsenmann, High Order Approximations in Space and Time of a Sixth Order Cahn-Hilliard Equation, No.41 - October, 2015.
- S. Gross, T. Ludescher, M.A. Olshanskii, and A. Reusken, Robust Preconditioning for XFEM Applied to Time-dependent Stokes Problems, No.40 - June, 2015.
- A. Lozovskiy, M.A. Olshanskii, V. Salamatova, and Y.V. Vassilevski, An Unconditionally Stable Semi-implicit FSI Finite Element Method, No.39 - May, 2015.
- M. Olshanskii, T. Heister, L.G. Rebholz, and K.J. Galvin, Natural Vorticity Boundary Conditions on Solid Walls, No.38 - April, 2015.
- L. Bertagna, A. Quaini, and A. Veneziani, Deconvolution-based Nonlinear Filtering for Incompressible Flows at Moderately Large Reynolds Numbers, No.37 - April, 2015.
- S.Burger, T. Franke, T.Fraunholz, R.H.W. Hoppe, M.A.Peter, and A. Wixforth Numerical Simulation of Surface Acoustic Wave Actuated Separation of Rigid Enantiomers by the Fictitious Domain Lagrange Multiplier Method, No.36 - March, 2015.
- E. Kikinzon, Yu.A. Kuznetsov, and Zh. Liu, Monotonicity in RT_0 and PWCF Methods on Triangular and Tetrahedral Meshes, No.35 - March, 2015.
- I.N. Konshin, M. Olshanskii, and Yu.V. Vassilevski, ILU Preconditioners for Non-symmetric Saddle Point Matrices with Application to the Incompressible Navier-Stokes equations, No.34 - March, 2015.
- T. Heister, M. Olshanskii, and L.G. Rebholz, Unconditional Long-time Stability of a Velocity-vorticity Method for the 2D Navier-Stokes Equations, No.33 - March, 2015.

**2014**

- S. Basting, A. Quaini, S. Canic, and R. Glowinski, An extended ALE method for fluid-structure interaction problems with large structural displacements, No.32 - October, 2014.
- A. Quaini, R. Glowinski, and S. Canic, Symmetry breaking and Hopf bifurcation for incompressible viscous flow in a contraction-expansion channel, No.31 - October, 2014.
- A. Chernyshenko, and M. Olshanskii, An adaptive octree finite element method for PDEs posed on surfaces, No.30 - August, 2014.
- K. Beleke-Maxwell, T. Franke, R.H.W. Hoppe, and C. Linsenmann, Numerical simulation of surface acoustic wave actuated enantiomer separation by the finite element immersed boundary method, No.29 - August, 2014.
- S. Gross, M. Olshanskii, and A. Reusken, A trace finite element method for a class of coupled bulk-interface transport problems, No.28 - June, 2014.
- Y. Qin, J.W. He, and R. Azencott, A second order variational approach for diffeomorphic matching of 3D surfaces, No.27 - March, 2014.
- M. Olshanskii, and D. Safin, A narrow-band unfitted finite element method for elliptic PDEs posed on surfaces, No.26 - January, 2014.

**2013**

- S. Basting, A. Quaini, R. Glowinski, and S. Canic, Comparison of time discretization schemes to simulate the motion of an inextensible beam, No.25 - December, 2013.
- A. Danilov, K. Nikitin, M. Olshanskii, K. Terekhov, and Yu. Vassilevski, A unified approach for computing tsunami, waves, floods, and landslides, No.24 - November, 2013.
- N.H. Sweilam, T.M. Al-Ajmi, and R.H.W. Hoppe, Numerical solution of some types of fractional optimal control problems, No.23 - November, 2013.
- R.H.W. Hoppe, and Z. Liu, Snapshot location by error equilibration in proper orthogonal decomposition for linear and semilinear parabolic partial differential equations, No.22 - November, 2013.
- W. Guo and J. Qiu, Hybrid semi-Lagrangian finite element-finite difference methods for the Vlasov equation, No.21 - October, 2013.
- W. Guo, R.D. Nair, and J. Qiu, A conservative semi-Lagrangian discontinuous Galerkin scheme on the cubed-sphere approach, No.20 - October, 2013.
- T. Xiong, J. Qiu , and Z. Xu, A parametrized maximum principle preserving flux limiter for finite difference RK-WENO schemes with applications in incompressible flows, No.19 - October, 2013.
- W. Guo, X. Zhong, and J. Qiu, Superconvergence of discontinuous Galerkin and local discontinuous Galerkin methods: eigen-structure analysis based on Fourier approach, No.18 - October, 2013.
- T. Passerini, A. Quaini, U. Villa, A. Veneziani, and S. Canic, Validation of an open source framework for the simulation of blood flow in rigid and deformable vessels, No.17 - October, 2013.
- S. Canic, B. Muha, and M. Bukac, Fluid-structure interaction involving multiple structural layers: theory and numerics, No.16 - October, 2013.
- M. Bukac, S. Canic, R. Glowinski, B. Muha, and A. Quaini, A modular, operator splitting scheme for fluid-structure interaction problems with thick structures, No.15 - October, 2013.
- B. Muha, and S. Canic, Existence of a solution to a fluid-multi-layered-structure interaction problem, No.14 - October, 2013.
- S. Canic, B. Muha, and M. Bukac, Stability of the kinematically coupled β-scheme for fluid-structure interaction problems in hemodynamics, No.13 - October, 2013.
- S. Canic, and B. Muha, A nonlinear moving-boundary problem of parabolic-hyperbolic-hyperbolic type arising in fluid-multi-layered structure interaction problems, No.12 - October, 2013.
- B. Muha, and S. Canic, A nonlinear, 3D fluid-structure interaction problem driven by the time-dependent dynamic pressure data: a constructive existence proof, No.11 - October, 2013.
- R.H.W. Hoppe, I. Yousept, Adaptive edge element approximation of H(curl)-elliptic optimal control problems with control constraints, No.10 - October, 2013.
- M. Olshanskii, and A. Reusken, Error analysis of a space-time finite element method for solving PDEs on evolving surfaces, No.9 - September, 2013.
- T. Franke, R.H.W. Hoppe, C. Linsenmann, L. Schmid, and A. Wixforth, Optimal control of surface acoustic wave actuated sorting of biological cells, No.8 - September, 2013.
- A. Gaevskaya, M. Hintermueller, and R.H.W. Hoppe, Adaptive finite elements for optimally controlled elliptic variational inequalities of obstacle type, No.7 - August, 2013.
- O. Boyarkin, and R.H.W. Hoppe, Optimal Control of Inductive Heating of Ferromagnetic Materials, No.6 - April, 2013.
- M. Olshanskii, A. Reusken, and X. Xu, An Eulerian space-time finite element method for diffusion problems on evolving surfaces, No.5 - April, 2013.
- M. Olshanskii, K. Terekhov, and Yu. Vassilevski, An octree-based solver for the incompressible Navier-Stokes equations with enhanced stability and low dissipation, No.4 - April, 2013.
- D. Braess, T. Fraunholz, and R.H.W. Hoppe, An Equilibrated A Posteriori Error Estimator for the Interior Penalty Discontinuous Galerkin Method, No.3 - April, 2013.
- A. Chertock, A. Kurganov, A.Polizzi, and I. Timofeyev, Pedestrian Flow Models with Slowdown Interactions, No.2 - March, 2013.
- A. Chernyshenko and M. Olshanskii, Non-degenerate Eulerian finite element method for solving PDEs on surfaces, No.1 - January, 2013.