# Global computation of an error with PETSc using block matrices

**URL:** <https://community.freefem.org/t/global-computation-of-an-error-with-petsc-using-block-matrices/2549>\
**Category:** General Discussion\
**Created:** [June 18, 2023, 7:04pm UTC](https://community.freefem.org/t/global-computation-of-an-error-with-petsc-using-block-matrices/2549 "2023-06-18T19:04:02Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![AzizTakhirov](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/aziztakhirov/32/26_2.png) [@AzizTakhirov](https://community.freefem.org/u/AzizTakhirov)\
**Post date:** [June 18, 2023, 7:04pm UTC](https://community.freefem.org/t/global-computation-of-an-error-with-petsc-using-block-matrices/2549/1 "2023-06-18T19:04:02Z")

</div>

Hello,  
I’ve adapted the part of the [stokes-block-2d-PETSc,edp](https://raw.githubusercontent.com/FreeFem/FreeFem-sources/master/examples/hpddm/stokes-block-2d-PETSc.edp) to conduct a convergence test with a manufactured solution.  
I need to have tgv=-1. The code works out OK, including the plots, but the errors are almost stagnant.  
I would appreciate it if anyone could point out the issue in the code. Thanks in advance.

[MWE.edp](https://community.freefem.org/uploads/short-url/yX4VgKgvjrQTAX5TTq5Hqf4aaa5.edp) (4.9 KB)

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<div class="post-metadata">

**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\
**Post date:** [June 19, 2023, 4:31am UTC](https://community.freefem.org/t/global-computation-of-an-error-with-petsc-using-block-matrices/2549/2 "2023-06-19T04:31:40Z")

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```diff
--- wrong.edp	2023-06-19 06:30:30
+++ right.edp	2023-06-19 06:30:26
@@ -90,8 +90,9 @@
 dC = vPb22(VhP, VhP);
 matrix<real> B = vPb12(VhP, VhV);
 Mat dB(dA, dC, B);
+Mat dD(dA, dC, B);
 {
- varf vonBorder([u, uB], [v, vB]) = on(1, u = u1exact, uB = u2exact);
+ varf vonBorder([u, uB], [v, vB]) = on(1, u = 1, uB = 1);
   real[int] onBorder = vonBorder(0, VhV, tgv=-1);
   real[int] onBorderPETSc;
   ChangeNumbering(dA, onBorder, onBorderPETSc);
@@ -100,7 +101,7 @@
 
 Mat dBT(dA, dC, B);
 Mat dS = [[dA , dB],
- [dBT', dC]];
+ [dD', dC]];
 real[int] rhsPETSc;
 {
   real[int] rhsV = vPb11(0, VhV, tgv = -1);
@@ -152,5 +153,5 @@
 if(mpirank == 0){
   savevtk("Error.vtu", ThGlobal, [solVGlobal,solVGlobalB],solPGlobal,communicator = mpiCommSelf);
   cout.scientific << "L2 v error = " << sqrt(int2d(ThGlobal)(solVGlobal^2+solVGlobalB^2)/ThGlobal.measure) << endl;
- cout.scientific << "L2 p error = " << sqrt(int2d(ThGlobal)(sumP^2)/ThGlobal.measure) << endl;
+ cout.scientific << "L2 p error = " << sqrt(int2d(ThGlobal)(solPGlobal^2)/ThGlobal.measure) << endl;
  }

```

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<div class="post-metadata">

**Author:** ![AzizTakhirov](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/aziztakhirov/32/26_2.png) [@AzizTakhirov](https://community.freefem.org/u/AzizTakhirov)\
**Post date:** [June 19, 2023, 6:10pm UTC](https://community.freefem.org/t/global-computation-of-an-error-with-petsc-using-block-matrices/2549/3 "2023-06-19T18:10:22Z")

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> [@prj](#):
>
> `solPGlobal`

Thank you!  
I see the problem now.