# Advanced Numerical Methods in Computational Mathematics

**Type:** Topics  
**Canonical URL:** https://scholariq.org/topics/advanced-numerical-methods-in-computational-mathematics/

## Facts

| Field | Value |
| --- | --- |
| Description | This cluster of papers represents advancements in finite element methods, particularly focusing on their application to fluid-structure interaction problems. The papers cover topics such as discontinuous Galerkin methods, high-order schemes, adaptive mesh refinement, stabilized methods, multiscale modeling, preconditioners, variational methods, and PDE-constrained optimization. |
| Domain | Physical Sciences |
| Field | Engineering |
| OpenAlex ID | t10339 |
| Works | 12 |

## Topic papers all

- [Two-medium treatment of heat transfer in porous media: numerical results for effective properties](https://scholariq.org/papers/two-medium-treatment-of-heat-transfer-in-porous-media-numerical-results-for/)
- [Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?](https://scholariq.org/papers/homogenization-via-formal-multiscale-asymptotics-and-volume-averaging-how-do-the/)
- [A numerical simulation of unsteady flow in a two-dimensional collapsible channel](https://scholariq.org/papers/a-numerical-simulation-of-unsteady-flow-in-a-two-dimensional-collapsible-channel/)
- [A control volume procedure for solving the elastic stress-strain equations on an unstructured mesh](https://scholariq.org/papers/a-control-volume-procedure-for-solving-the-elastic-stress-strain-equations-on-an/)
- [Augmented Lagrangian Active Set Methods for Obstacle Problems](https://scholariq.org/papers/augmented-lagrangian-active-set-methods-for-obstacle-problems/)
- [On the Application of the Continuous Galerkin Finite Element Method for Conservation Problems](https://scholariq.org/papers/on-the-application-of-the-continuous-galerkin-finite-element-method-for/)
- [Group-wise construction of reduced models for understanding and characterization of pulmonary blood flows from medical images](https://scholariq.org/papers/group-wise-construction-of-reduced-models-for-understanding-and-characterization/)
- [CUPyDO - An integrated Python environment for coupled fluid-structure simulations](https://scholariq.org/papers/cupydo-an-integrated-python-environment-for-coupled-fluid-structure-simulations/)
- [A finite element implementation of the isotropic exponentiated Hencky-logarithmic model and simulation of the eversion of elastic tubes](https://scholariq.org/papers/a-finite-element-implementation-of-the-isotropic-exponentiated-hencky/)
- [Approximate solution of the Bagley–Torvik equation by hybridizable discontinuous Galerkin methods](https://scholariq.org/papers/approximate-solution-of-the-bagley-torvik-equation-by-hybridizable-discontinuous/)
- [Variationally mimetic operator networks](https://scholariq.org/papers/variationally-mimetic-operator-networks/)
- [Applications of mechanical engineering mathematics : Solving Neumann problem with discontinuous coefficients](https://scholariq.org/papers/applications-of-mechanical-engineering-mathematics-solving-neumann-problem-with/)

## Topic primary papers

- [A control volume procedure for solving the elastic stress-strain equations on an unstructured mesh](https://scholariq.org/papers/a-control-volume-procedure-for-solving-the-elastic-stress-strain-equations-on-an/)
- [On the Application of the Continuous Galerkin Finite Element Method for Conservation Problems](https://scholariq.org/papers/on-the-application-of-the-continuous-galerkin-finite-element-method-for/)
- [Approximate solution of the Bagley–Torvik equation by hybridizable discontinuous Galerkin methods](https://scholariq.org/papers/approximate-solution-of-the-bagley-torvik-equation-by-hybridizable-discontinuous/)

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Source: ScholarIQ — public research metadata, principally OpenAlex. See https://scholariq.org/sources/ for provenance and https://scholariq.org/methodology/ for what these figures mean.