| Abstrak |
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Abstract | The numerical approximation of the Laplace equation with inhomo-
geneous mixed boundary conditions in 2D with lowest-order Raviart-Thomas mixed
¯nite elements is realized in three °exible and short MATLAB programs. The ¯rst,
hybrid, implementation (LMmfem) assumes that the discrete function ph(x) equals
a + bx for x with unknowns a 2 R2 and b 2 R on each element and then enforces
ph 2 H(div; ) through Lagrange multipliers. The second, direct, approach (EBmfem)
utilizes edge-basis functions (ÃE : E 2 E) as an explicit basis of RT0 with the edgewise
constant °ux normal ph¢ºE as a degree of freedom. The third ansatz (CRmfem) utilizes
the P1 nonconforming ¯nite element method due to Crouzeix and Raviart and then
postprocesses the discrete °ux via a technique due to Marini. It is the aim of this pa-
per to derive, document, illustrate, and validate the three MATLAB implementations
EBmfem, LMmfem, and CRmfem for further use and modi¯cation in education and
research. A posteriori error control with a reliable and e±cient averaging technique is
included to monitor the discretization error. Therein, emphasis is on the correct treat-
ment of mixed boundary conditions. Numerical examples illustrate some applications
of the provided software and the quality of the error estimation. |
Dosen & Pendukung 
