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Chad Westphal


P.O. Box 352
Dept. of Math and CS
Wabash College
Crawfordsville, IN 47933

(765) 361 6101
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Research Overview :

I am a numerical analyst with broad interests in applied mathematics. Most of the work that I am currently involved with is within the context of finite element methods for partial differential equations (PDEs) in one form or another. I also foster an interest in developing predictive simulation models for stochastic systems, including election models, infectious diseases, and baseball -- I've even developed an undergraduate project-based course on stochastic simulation.

Doing research with undergrads? Check out Ethics for Undergraduate Researchers in Mathematics, a side-project developed with Mike Axtell.

I spent the 2018-2019 academic year as Distinguished Visiting Professor in the Department of Mathematical Sciences at the U.S. Air Force Academy.

If you're interested, have a look at my CV, but it's probably outdated.

Current and Recent Projects:
  • Adaptively weighted finite element methods
  • First-order system LL* methods
  • Finite element methods for fully nonlinear problems
  • Stochastic simulation of game theoretic models
  • Infectious Disease Modeling


  • C.R. Westphal, "A Newton Div-Curl Least-Squares Finite Element Method for the Elliptic Monge-Ampere Equation," Comp. Meth. Appl. Math., 19-3, pp. 631-643, 2019.

  • T. Nguyen and C.R. Westphal "Soccer Penalty Kicks and the Mixed-Strategy Nash Equilibrium: An Evolutionary Approach," submitted.

  • B. Hayhurst, M. Keller, C. Rai, X. Sun and C.R. Westphal, "Adaptively Weighted Least Squares Finite Element Methods For Partial Differential Equations with Singularities," 13-1, pp. 1-25, 2018.

  • E. Lee, T.A. Manteuffel and C.R. Westphal, "FOSLL* for Nonlinear Partial Differential Equations," Siam. J. Sci. Comput., 37-5, pp. S503-S525, 2015.

  • Y. Sun and C.R. Westphal, "An Adaptively Weighted Galerkin Finite Element Method for Boundary Value Problems," CAMCoS, 10-1, pp27-41, 2015.

  • S. Bidwell, M.E Hassell and C.R. Westphal, "A Weighted Least Squares Finite Element Method For Elliptic Problems with Degenerate and Singular Coefficients," Math. Comp., 82, 672-688, 2013.

  • B. Kraynik, Y. Sun and C. Westphal, "Multiscale Adaptively Weighted Least Squares Finite Element Methods for Convection Dominated PDEs," Involve, 5-1, 39-49, 2012.

  • M. Axtell and C. Westphal, "Ethics for Undergraduate Researchers", Notices of the AMS, 59(3), 2012.

  • Z. Cai and C.R. Westphal, "An Adaptive Mixed Least-Squares Finite Element Method for Viscoelastic Fluids of Oldroyd Type," J. Non-Newt. Fluid Mech., 159, pp 72-80, 2009.

  • Z. Cai and C.R. Westphal, "A Weighted H(div) Least-Squares Method for Second-Order Elliptic Problems," SIAM J. Numer. Anal., 46, pp 1640-1651, 2008.

  • E. Lee, T. Manteuffel and C.R. Westphal, "Weighted-Norm First-Order System Least Squares for Problems with Three Dimensional Edge Singularities." SIAM J. Numer. Anal., 46, pp 1619-1639, 2008.

  • C. Westphal, "A Least-Squares Finite-Element Method for Viscoelastic Fluids," Proc. Appl. Math. Mech. (PAMM), 7(1), 1025101-2, 2008.

  • C. Westphal, "Teaching Time Savers: Encouraging Contact Early in the Semester," FOCUS, 27(6), 2007.

  • E. Lee, T. Manteuffel and C.R. Westphal, "Weighted-Norm First-Order System Least Squares for Problems with Corner Singularities." SIAM J. Numer. Anal. 44, pp. 1974-1996, 2006.

  • T. Manteuffel, S.F. McCormick, J.G. Schmidt and C.R. Westphal, "First-Order System Least Squares (FOSLS) for Geometrically Nonlinear Elasticity." SIAM J. Numer. Anal., 44, pp. 2057-2081, 2006.

  • C. Westphal, "First-Order System Least Squares (FOSLS) for Geometrically Nonlinear Elasticity in Nonsmooth Domains." Ph.D. Thesis, University of Colorado, 2004.

  • Teaching Overview :

    Since 2004, I've been in the Department of Mathematics and Computer Science at Wabash College. I've taught a lot of courses here and a few elsewhere.

    Spring 2021 Courses:
    MAT 112 Calculus II
    CSC 211         Data Structures
    MAT 344 Complex Analysis

    Past Courses:
    MAT 337 (=CSC 337) Numerical Analysis
    MAT 344 Complex Analysis
    MAT 324 Partial Differential Equations
    MAT 224 Differential Equations
    MAT 223 Linear Algebra
    MAT 112 Calculus II
    MAT 111 Calculus I
    MAT 110 Calculus I with Precalculus Review
    MAT 010 Precalculus with an intro to Calculus
    MAT 108 Discrete Mathematics
    MAT 003 Precalculus
    CSC 235         (=MAT 235=PHY 235) Stochastic Simulation
    CSC 211         Data Structures
    CSC 112         Advanced Programming
    CSC 111         Intro to Programming (seriously cool class photos)
    C&T 201         Cultures and Traditions
    FRC Freshman Colloquium, Enduring Questions
    MATH 141         Calculus I (USAFA)
    MATH 245         Differential Equations (USAFA)
    MATH 469         Partial Differential Equations (USAFA)
    APPM 4660    Numerical Analysis II (University of Colorado)
    APPM 4650    Numerical Analysis I (University of Colorado)
    APPM 2350 Calculus III for Engineers (University of Colorado)
    APPM 1350     Calculus I for Engineers (University of Colorado)
    PHY 1214 General Physics II (Tulsa Community College)
    PHY 1114 General Physics I (Tulsa Community College)

    Personal :
    The Westphal family consists of Chad and Amy, our two kids, Henry and Adah, and our dogs. Have a look at our (outdated) photos page if you're interested.

    We live in Crawfordsville, Indiana, a nice small town an hour from Indianapolis. Before moving here in the summer of 2004, we lived in Lafayette, Colorado, just outside the People's Republic of Boulder. Before that we lived in Tulsa, Oklahoma. We've also spent a few fantastic sabbaticals in Colorado.

    I spend most of my time either working or with my family, as I should. Theoretically, if I had lots of free time I'd spend it woodworking, snowboarding, mountain biking, skateboarding and playing disc golf. In what seems like another lifetime, I was an avid skateboarder. Now I just enjoy getting outdoors in any way I can. I'm a bit of a presidential history buff, but only enough to be annoying. I sometimes pretend I can play the banjo, but I'm really much better at listening to bluegrass and classic country music.

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    --CRW, 2016